I got a Departmental Studentship at 'another' Uni (i.e. not where I did my Masters), so it does happen. It's hard to generalise I suppose, but I certainly wouldn't assume students already at a Uni will automatically be first choice. (Not sure why Uni-funded scholarships would be any different from externally funded scholarships, by the way - surely the Uni chooses the successful applicants in just the same way?)