My guess, the various clues all came in focus for the crew and they decided to go--the radio comment by UA, the tower saying the runway was clear when they thought it was not and PAL flashing his lights. They just starting doubting themselves very late. They can't have mistaken the UA comment--they were the only ones it could possibly have applied to.
Without the CVR, we'll never know the truth sadly.
As to the UA and PAL crews, what would expect them to do? Taxi back and leave 600 pax stranded. Close call, move on
GF