I've been working in a research setting for the past year. I work at UVA that has a very large amount of research projects between the undergraduate school and the medical school.
As far as I know there are 2 vets that work here and you are right that they do a lot of paperwork, however, there are many other oportunities and perks to the job. The vet for my building (I work in the Biology Department) has a tiny little office with no windows and does have to spend a lot of time pushing papers, also the only animals we have in the building are rodents (rats, mice, hamsters) and a couple puffer fish. But, he also teaches Animal Physiology once a year and has an active lab working on research (He obviously has a DVM and a PhD). So he is a good example of what you can do with a DVM - teach, research, lab animal medicine - basically, he has three jobs.
The second vet is in charge of the vivarium at the medical school. As far as I know she doesn't do research, nor does she teach. But, she does have a huge vivarium to take care of. In this vivarium there are the usual mice, rats, hamsters, but there are also swine, rabbits, cats, dogs (yes - this makes me a little sad) and even primates. So, she does have the benefit of working with a diversity of animals. I think this is more of what intended when someone suggested lab animal medicine as an option for someone with an interest in zoo/exotics.