Anaphoric ambiguity of the week

From David Axe, "How Trump Could Bypass a Key Vaccine Safety Valve", Daily Beast 10/1/2020 [emphasis added]:

If the Trump administration tries to push out a novel coronavirus vaccine before it’s fully tested, there are three committees of independent experts who could stand in its way. […]

These committees—two in government and one in the private sector—keep tabs on vaccine-testing, sign off on new drugs and vaccines, and advise the government on how to deploy a new inoculation. But it remains to be seen just how much clout they have if the government decides to skirt science and rush out an Election Year miracle. […]

Of course, it’s possible the Trump administration doesn’t care about the controversy that might result from pushing a vaccine before it’s ready. Even if all three committees voted against a vaccine, the FDA might approve and distribute the vaccine, anyway. The administration has steadily been consolidating control over the vaccine-approval process, all while Trump continues to promise a vaccine before most experts expect one to be ready.

The problem is that the advisory committees mostly derive their authority from government agencies’ rules—and the same agencies can, with varying degrees of effort, change those rules. “The FDA and CDC advisory committees are that—advisory,” Lurie said. “There’s no requirement for them to follow them.”

That's Peter Lurie, President of the Center for Science in the Public Interest and a former member of the Vaccines and Related Biological Products Advisory Committee (VRBPAC) at the U.S. Food and Drug Administration.

Since this is Language Log, not Vaccine Safety Log, the point of the quotation is the tricky reference of the two instances of them in the bolded phrase at the end. It's obvious to a human reader that the meaning is something like "There's no requirement for the government agencies to follow the advisory committees", or maybe "… to follow the rules that the advisory committees derive their authority from".

This is a sort of double Winograd Schema example. Multiple pronoun puzzles are not uncommon — here are a few examples from COCA:

Kevin and I were ice skating, and he got all Tonya Harding on the rink manager when he told him he couldn't have snacks on the ice. When God called Moses to be his agent to bring Israel out of Egypt, he told him, " See, I have made you like God to Pharaoh, Rex said that he didn't understand, but Skywalker told him that even if he told him the truth, Rex would not believe him.