It was a big coup when a nonprofit medical trade group landed Bill Clinton as a speaker at its 2010 annual conference in Chicago -- so big that some members wondered how the former president was being paid.

Not to worry, members of the Radiological Society of North America were told: An anonymous donor footed his bill.

The $150,000 fee was a mere fraction of the $48 million Clinton took in from 215 speeches between 2009 and 2013, while his wife was secretary of state. Who paid Clinton and why they thought it was a fair bargain may never be known — but government watchdogs say it is a prime example of how elusive accounting can be for the ex-president's eye-popping earnings.

It was clear, however, that the husband of America's top diplomat was not chosen for his medical expertise.

“This issue has to be resolved. There has to be an answer as to who gave the money."

- Matthew Whitaker, Foundation for Accountability & Civic Trust

“I think this is interesting that you would ask me to come and speak today to a group of people from all over the world, and everyone of you knows more about the subject than I do,” Clinton said at the beginning of his 45-minute address to an audience of 4,250.

Dr. Sam Friedman, a radiologist from Columbia, SC., said at first he was “peeved” when he heard Clinton was paid $150,000 for the “rambling” speech, during which Clinton took several “gratuitous shots” at Republicans and blamed U.S. doctors for many of the healthcare problems in third world countries. When he and like-minded members made their objections known to the organization, they were told the fee was paid by an “anonymous” donor. 

Radiological Society of North America spokesman Marijo Millette told FoxNews.com the group “strives to provide compelling speakers that will satisfy the educational needs and special interests of a diverse audience.”

Millette would not comment on Friedman's claim, which was also reported by trade media, but said Clinton's fee and travel expenses were paid to the Harry Walker Agency, which represents Clinton. The organization’s 990 forms, filed with the Internal Revenue Service and required to maintain its 501(c)3 status, do not list any payment to Clinton or his representative. Neither the executive director nor three executive board members contacted by FoxNews.com would divulge who paid Clinton's fee.

Matthew Whitaker, executive director of the Foundation for Accountability & Civic Trust, a Washington-based, non-partisan campaign and ethics watchdog group, said the anonymous donation “opens up a Pandora’s box of questions including who funded this speech and what their motivations were.”

“This issue has to be resolved," Whitaker told FoxNews.com. "There has to be an answer as to who gave the money. “It has the smell of someone trying to move money through an organization to curry favor with the former president. It also calls into question almost every speech Bill Clinton has made and who the ultimate funder is.”

Neither Clinton's representatives at Harry Walker nor at the Clinton Foundation responded to a request for the name of the mystery sponsor. It was not clear if other speeches by Clinton were similarly funded by anonymous third parties.

Tom Fitton, president of Judicial Watch, a Washington D.C.-based government watchdog foundation, said much of the $48 million Bill Clinton made from 215 speeches during the time Hillary Clinton was Secretary of State went to the Clintons' personal coffers, not to the foundation. Federal disclosure forms filed by Hillary Clinton for 2010 record her husband’s compensation as $150,000 from the Oak Brook, Ill.-based group, but critics say the lack of transparency about where the money really came from raises serious questions.  

“Bill and Hillary Clinton are married, so under the law, paying him for a speech is like giving money directly to her – to the Secretary of State,” Fitton said. “I cannot think of a comparable ‘pay to play’ scandal.”

Clinton gave 542 speeches around the world between 2001 and 2013, earning $104.9 million, and delivered another 53 speeches between January 2014 and May 2015, earning an additional $13.5 million, according to reports by Fox News and the Washington Post. The former president's speaking fees have ranged from $28,100 for a 2001 talk at the London School of Economics to $750,000 for a 2011 appearance at an event for Swedish communications company Ericsson.

While Clinton's knowledge of world events and charm as a raconteur is well-documented, critics doubt the sky-high fees are doled out by anonymous parties for sheer entertainment value.

"These donors don't cut checks because they want to hear a brief speech," said Sean Davis, co- founder of The Federalist, a conservative online magazine. "They do it to gain access or favors from the Clintons. The Clintons owe voters a clear explanation of who is funneling them this money and why.”