I agree with this, that is definitely a legit backup option. But if you can, I think it would be better to have 1 letter coming from the lab, for the reasons nyanko stated. I think it's an exception rather than the rule that the PI won't collaborate with someone else to write your letter. At least of the people I know who worked more with post-docs/grad students than the PI themselves, the PI was well aware of the fact that they didn't know the applicant all that well even if they wanted to write a positive letter. In almost all cases, the PI either just asked the post-doc for info in-person/via email OR just had the post-doc write a draft that the PI then edited and sent out.
If you work in a lab with DVM's it's one thing, but otherwise, you're using up 2 precious LORs coming from 1 experience that's not veterinary. Esp if you're a traditional applicant, most vet schools want 1 academic reference and at least one vet reference. For the places that you can designate 3 LOR's, I would personally rather have a GOOD letter signed by the PI, rather than have to pick between the luke-warm generic one by the PI or the good letter by the non-PI.
Also, Post-doc wouldn't be so bad but I'd be a little bit wary of getting a letter from a grad student... because even if they're not your peers per se, they're not technically researchers yet. It's kinda like if you're shadowing at a teaching hospital, and you're asking a 4th year student that you followed every week to write for you because that 4th year knows you far better than any of the attendings. Post-docs, residents, and even interns at least have gotten through the schooling and are doctors.