I have actually missed connections coming into LAX and SFO because I had to undergo secondary screening by customs*. Both times, UA re-booked me at no charge on another flight. The first time was when I was 2P, so it's not a status thing I think.
*Once you got that US work Visa in your passport they give you the proverbial rubber glove every time when entering from overseas... That GOES card is worth its weight in DEQMs.... ^