Vet schools do not care where you went undergrad. They may care if you are IS or OOS due to the number of seats they have. After that it is based on GPA, GRE (if required - most this is going away) and experience to get an interview. If they do interviews then those add in. All the schools you mention get their students into vet schools just as well as the others do and it isn’t a disadvantage. The standard words are go to the school where you can get the best grades, get out with the least debt and have a good fit.
My son didn’t have much of a plan B since he got in the early admit program and was sure he was going to vet school. Probably a PhD in immunology would have been hi plan B.