My pets are most beloved members of my family. I want only the very best care possible for them. If a medical procedure is a type I wouldn't let a student do for me, then I wouldn't let a student do it for my pet. Pet owners are owed the courtesy of information on who will be doing what to/for their pets. You pick a certain vet for his/her standards and reputation and you are paying fees for their knowledge and expertese, not for the education of a student. 

I believe informed owner consent should be instituted and made to be a legal binder in all cases of vet student involvement.