Everything said so far it true. But to put it into an international context, you can get jerked around most anywhere if you don't follow the procedure that the inspector is looking for.
In Luton, two hours waiting for customs to arrive (at 3AM), in Stanstead, they wouldn't let us take soup through to the aircraft (outbound), In Nice, an insufferable SAFA check, in China, I had a visa refused, in Riyadh, a four hour delay to insure we really were approved to depart.
The USA is simply par for the course, so always call ahead before you leave home base, and call from the airport prior to US entry.
FR