Can an American citizen have his/her travel privileges reviewed?

They cannot be denied entry in to the US assuming they can prove who they are and their citizenship - regardless of their passport status. But obviously having a valid passport makes that easier. There are some cases with dual citizenship that can cause you to be turned away, but in general, you have a right of entry as a US citizen. That doesn’t mean you can’t be searched, detained, or arrested, but you have the right of entry.

“Travel privileges” doesn’t necessarily relate to being allowed to travel. I suspect it’s something like Global Entry status, which apparently is being rescinded from various U.S. citizens who are Muslim.

If that be the case as stated, the courts are going to have a field day with it.

From your cite:

My immediate reaction to the organizers’ statement was that Canada had informed Mr. Khan that he would not be permitted to enter the country, rather than that the US had told him he couldn’t leave.

Why would Canada refuse him?

I don’t think it’s that he can’t leave, but that he hears he might experience issues on returning.

It’s not Canada that is reviewing Mr. Khan’s travel privileges. From the Washington Post, via Canada’s National Post:

Although it is probably not the case here, it is now possible to have your US passport revoked if you have unpaid taxes:

From Forbes among others

//i\

Who did he hear it from? An anonymous tipster? A government official? Written notice? A little bird? It sounded like bullshit when I first heard it and the fact that he refuses to clarify makes me believe it is bullshit.