Yes, your qualifications are the most important, but saying that it does not matter if you are in state or out of state is a flat out lie or maybe just naive.
All it takes is a quick look at statistics among the individual vet schools to see that.
I will use UGA, for an example, here is the link to their stats:
http://vet.uga.edu/admissions/statistics
637 "at large" or out of state applicants applied and out of those 15 were enrolled
244 Georgia residents applied out of those 80 were accepted. Now just that difference it is plain to see that being a Georgia resident gave you increased odds of being accepted.
Now on that same page, they also have basic stats of those "at large" vs. those that are Georgia residents... The Cum. GPA for OOS: 3.68, for Georgia residents: 3.55. Science GPA for OOS: 3.67, for Georgia residents: 3.44.
This is just one school, but if one does some looking this is similar across the board minus a few schools that accept similar numbers of OOS as they do in-state, but even at those schools you have less people applying that are residents of that state than you do that are non-residents. So if you have 300 people apply as an in-state student for 50 seats and 800 people apply as OOS students for 50 seats, you would want to be in that in-state pool. There is just simply less competition.
Obviously, being in-state does not make up for poor GPA's or GRE scores, but for those that are sitting at average, being IS can give you a significant advantage and was actually recommended to me in a file review by one of the veterinary schools.