I am assuming that somewhere in the small print on your ticketing agreement that you have forfeited that fourth amendment.
Nope, not on American Airlines. I looked.
I’ll post a URL when I get home.
As promised, here it is:
American Airlines Condition of Carriage
There is a clause here that I missed: American may refuse to transport you, or may remove you from your flight at any point, for one or several reasons, including but not limited to the following:
4. Refusal to permit a search of person or property for explosives or for deadly, controlled, or dangerous weapons, articles or substances.
So, you are correct: you may be refused transport if you don't do this. But, the only penalty for non-compliance in this contract is removal from the flight, or not boarding in the first place.
At no point are you explicitly consenting to a search in advance.