IMF chief Christine Lagarde wants the people of Greece to pay their taxes. The problem? She doesn't really pay taxes herself.

Last Friday, The Guardian ran an interview with Lagarde, in which she suggested that she wasn't exactly full of sympathy for the people of Greece, despite the painful austerity measures currently in place there.

"As far as Athens is concerned, I also think about all those people who are trying to escape tax all the time," Lagarde told The Guardian. "All these people in Greece who are trying to escape tax."

It may have been a poor choice of words. On Tuesday, The Guardian reported that Lagarde herself pays no taxes on her yearly $467,940 salary, or the $83,760 allowance that comes on top of it.

Lagarde's tax-free status is typical of United Nations employees -- as CNBC notes, Lagarde's predecessor Dominique Strauss-Kahn had an identical arrangement when he had the job -- but that hasn't stopped irate commenters from piling onto Lagarde's Facebook page, where the IMF chief now appears to be doing a bit of damage control.

"As I have said many times before, I am very sympathetic to the Greek people and the challenges they are facing," reads a post from Lagarde, dated May 26.

"That's why the IMF is supporting Greece in its endeavor to overcome the current crisis and return to the path of economic growth, jobs and stability," Lagarde's post reads. "An important part of this effort is that everyone should carry their fair share of the burden, especially the most privileged and especially in terms of paying their taxes. That is the point I was emphasizing when I spoke to the Guardian newspaper as part of a broader interview some time ago."

Few people, meanwhile, seem to be questioning Lagarde's point that tax evasion is incredibly common in Greece, thanks in part to a permissive legal environment and a tax code thick with loopholes.

In March, an official with the European Commission estimated that Greece might have as much as 8 billion euros, or $9.95 billion, in collectible unpaid tax revenue.