Last month, financial crimes prosecutors charged him with falsifying official data. The rationale behind such charges has not yet been released, but he may be convicted of breach of faith - a crime that usually applies to those who embezzle or misuse public funds. If he is, he could face at least five years in jail.
Georgiou, 52, says he did nothing wrong and merely applied EU statistical standards, such as ensuring data-collectors are free of political influence. "That this is happening in the middle of the euro zone is a strange and surreal experience," he said. "I am being prosecuted for following the law."
His supporters, including EU partners who are bankrolling Athens with hundreds of billions of euros, say the affair reflects continuing political reluctance in Greece to confront many of the country's structural flaws.
Eurostat, the EU's official statistics authority, has rushed to Georgiou's defence, issuing public statements in his support. A spokesman for the German finance ministry said he knew of the investigation, but had heard nothing about Germany's alleged part.
"I don't even know the accusations. Nonsense," he said.
The current Greek government has also backed Georgiou, although it is clearly hesitant to interfere in the judicial process.
"The outside world doesn't understand and, to be honest, we have a huge difficulty explaining to our partners what is happening here," said a senior Greek finance ministry official on condition of anonymity.
"What we stress is that we stand behind the current numbers underpinning the economic programme. They have been verified by Eurostat and we have full confidence in Mr. Georgiou."
Government officials say part of the problem with Greece's statistical service was that, until recently, it was controlled by the finance ministry and at the mercy of ministers. In the past, some may have wanted to keep GDP low to collect more EU subsidies, while others wanted to boost GDP to keep the deficit ratio within EU rules, said officials.
Eurostat regularly used to give Greece's numbers "reservations", meaning it doubted their validity.
In 2004, then-finance minister George Alogoskoufis told Brussels that Greece had under-reported its budget deficit for years, including for 2001, the year it joined the euro zone.
Two years later, Greece stunned its European partners again by announcing that it was revising up its GDP by 25 percent after including money laundering and prostitution. Eurostat objected and approved only a 9 percent revision, but not before Greece had been ridiculed by international media.
"Greece managed to get by somehow, with reservations on its statistics, for some time," said Georgiou, who has a Ph.D. in economics from the University of Michigan and held senior posts at the International Monetary Fund from 1989 to 2010. "It was an approach and a culture. But it led to a wiping out of the credibility of the statistics of the country."
That credibility suffered further with a new finance minister. Socialist George Papaconstantinou announced in late 2009 that the budget deficit would come to 12.7 percent of GDP instead of a previously estimated 6 percent. He blamed his Conservative predecessor.
Eurogroup head and Luxembourg Prime Minister Jean-Claude Juncker told reporters in Brussels at the time: "The game is over - we need serious statistics."
The revision was followed by another new deficit estimate of 13.6 percent in April 2010.
It was at that point, as part of an international bailout that rescued Greece from bankruptcy, that Papaconstantinou created a new, independent statistics authority and brought in Georgiou.
The new statistics boss, plucked from his career in Washington, came with a reputation for a mild manner, a fondness for pastel ties, and a black belt in Jujitsu.
In October 2010, he re-examined the 2009 budget deficit figure with Eurostat and revised it again, this time to 15.4 percent.
Alogoskoufis declined to comment on how the statistics service had operated when he was minister. Papaconstantinou says it was during his tenure that the agency started functioning without political interference. As for the charges against Georgiou, he said, the final arbiter of the veracity of any EU member's data is Eurostat, whose rules national statistical agencies are required to apply. "I therefore fail to see how and why this is an issue for the Greek courts."
Georgiou compares the task of reshaping the authority to Hercules cleaning the Augean stables - which the mythological hero achieved by rerouting two rivers.
"I said we are going to do things differently, according to European law and international statistical standards - no ands, ifs or buts," he said. As well as his martial arts expertise, he has written a book on the ancient Greek sport of Pankration, a blend of boxing and wrestling with hardly any rules.
But there were challenges at ELSTAT from the start, he says. Board members included some of those who had applied for the top job, as well as an appointee of the finance minister, an appointee of the central bank and a labour union representative.
Board members wanted more direct involvement in producing numbers. Georgiou insisted that should be solely the work of statisticians, both Georgiou and board members said.
"Some board members went to the staff and told them they wanted to help Greece minimise the deficit and debt. That's a no-no," Georgiou said. "I explained that the technical staff had to do their jobs independently."
He said that in the past two and a half years, Greece has produced sets of figures five times without any Eurostat reservations - for the first time in years. Eurostat confirmed the 2009 deficit figure after scrutiny.
But clashes continued, including with the ELSTAT trade union, whose president Nikos Klouvatos has asked for Georgiou to step down pending his trial.
"He wanted board members to be decorative plants in the room," said Klouvatos. "He wanted to change everything and we told him we agree but he had to do it slowly."
The finance ministry official said Georgiou may not at first have received full support. "It looks like the first attempt was to have an internationally minded president who could talk convincingly with foreigners but to surround him with people controlled by the government," he said.
In September 2011 then-finance minister Evangelos Venizelos dismissed the ELSTAT board, and in April 2012 a new law created an advisory council instead.
Since then, former board members have alleged that Georgiou deliberately inflated the 2009 budget deficit, leading Greece's euro zone partners to demand tougher austerity measures in return for bailing out the country. One of their number, an applied econometrics professor from the University of Thessaloniki, insists her concerns are technical.
"They say I am politically motivated and vengeful because I was fired. This is nonsense," said Zoe Georganta. "I noticed anomalies with the numbers and I expressed my doubts."
Georganta says the draconian austerity measures imposed on Greece are still based on incorrect figures. Her calculations show that Greece's GDP "is underestimated by at least 30 percent," she said. "I estimated that our (2012) deficit is not over 4 percent of GDP."
Georgiou rejects those figures and the allegation that he overstated the deficit. The IMF and the EU put Greece's deficit in 2012 at 6.6 percent of GDP.
In Greece, battle is joined. One newspaper called Georgiou the Trojan horse of the international lenders. But former premier George Papandreou slammed the prosecutors, saying the attack on the statistics boss was an assault on his own days in office, and that earlier statistics officials had fiddled the figures for years.
The union of Greek prosecutors hit back, calling Papandreou's statement an unacceptable meddling in justice.
It could take a year or more for the case to come to court. Given investigators have not yet finished their work, it remains possible the charges will be dropped.
Georgiou says the country needs serious statistics. "Serving the national interest is to produce official statistics according to international statistical standards, correct methodology and EU law. This is how we best serve our country," he said.
"I came here because I loved Greece and I still love it despite everything."
(Additional reporting by Gernot Heller in Berlin; Editing by Richard Woods and Sara Ledwith)