No they could not. You must enter and exit country on the same Nationality of passport. Sadly she made the mistake after a long flight of entering on her UK passport. She overstayed and was fined. Not a good result but the only outcome possible. Like I said in the case of my daughter, she was questioned by the IO and advised by her to enter on her American passport because her expired passport could not be used to leave, nor could her American with no entry stamp. Trying to help her in case she was not able to renew her Thai passport. She chose to enter on the expired passport and did get the new one for departure. She was able to show the old one with the entry stamp on departure.
I might add that this same daughter once came home from university for 3 weeks at Christmas and was tired from the long flight and entered on her US passport and got the visa waiver. If she had done the same thing in the summer she would have been on a 2 month overstay as she stayed 3 months. For sure maybe on the advice of the IO she entered on her UK passport.