Is a verbal job offer and agreement between boss and employee at a community college legally binding in Texas?

My daughter applied, interviewed, and was voted by a hiring committee as the best candidate for a BA position. She is a current classified employee there and this would have been a promotion for her. Her boss-VP of the college-offered her the position. He told her the job was hers if she wants it. She said yes. He signed the Request to hire paperwork and so did the members of the the hiring committee. When paperwork was sent to HR, the Associate VP said no she didn't meet qualifications but she actually does with experience or never would have made it through the screening process. HR person is new in position and refuses to count daughter's work experience and BA in communications degree as usual equivalent qualifications as stated on job posting.She said VP spoke out of turn with offer.