Sure.
All you need to do is get a suitable O2 tank, say 300 cubic feet. I am not sure what that rental will set you back. You will also want to have a fill whip. If you get a basic analog one with an O2 adaptor attachment, you can get one for under $400. A digital fill whip kit is around $800.
When you figure the cost of the O2 tank, remember that you will only be able to use about half of the gas in it with just a fill whip at your disposal. That is because you can only fill your scuba tank up to the PSI left in the O2 tank. You can either return the half full tank and get a new one, or you can get several of them and use them in a series, taking the most empty one first and then working your way up to the fullest. You can also purchase a Haskell booster so that you can use the whole thing. Of course, at about $3,000 for the portable model, you will want to be mixing a lot of nitrox to make that worth while.
Remember that you must top off the fill with Grade E air, so you will want to make sure that your compressor has that kind of ultra high quality filter. (Remember, fire departments do not need Grade E air for their purposes.)
So, you are right. A nitrox diver can get fills without needing a shop to do it.