She can. Of course, there is no guarantee she'd be allowed back into the UK afterwards.
Unless she has a visa in advance, it will always be up to the discretion of the immigration officer on the day. None of us will be able to tell you if she will be allowed in or not.
That being said, nothing sounds off to me. But again, I'm not sure what (if anything) is different for a Mexican. I only know the rules for Americans.
