If you are a citizen of the United States of America, and you are returning to the United States from a foreign country, Customs and Border Patrol are not allowed to deny you entry to the United States of America.

Of course the caveats - if you, as the citizen, have an outstanding warrant, they can arrest you. They can take your electronics. They can delay you. They can put you in a room by yourself for some period of time. But they can’t deny you entry without some kind of legal reason. They can’t hold you indefinitely.

It just comes down to how much the citizen is willing to be inconvenienced.

And I believe any American with any felony on their record will have trouble visiting Canada. I once traveled with a guy who had a felony assault conviction from a college bar fight 15 years prior. They wouldn’t let him in.

But they will lie to you and tell you they won't let you in.

They will also lie to you and tell you they have the power to cancel your passport.

I've had them pull both 'tricks' on me. Not a lot of people are well versed on their rights and without access to a lawyer it would be easy to believe a federal officer when they tell you these things. If you believe what a federal officer tells you, which is probably most Americans, being told you won't be let in unless you do X is going to be taken literally as 'unless I do X, I am denied entry to the country.' They will simply comply on the basis of a fraudulent lie, which I might add a material lie like this is a felony if a normal citizen says it to a federal agent.