The answer is no. To be considered a finished basement there must be a wall covering around the "finished" part of the basement. If it were just concrete, well that is an unfinished basement.
I have seen a lot of goofy things done including adding a 1/2" of plaster to all of the outer walls, putting drywall on basically shims, adding faux brick panels all around and probably countless other things. Those would be considered suitable for a finished basement.
Really the only other requirements on a finished basement are minimal lighting available (including switched at entrance) and outlets every 6 feet.
So no you can't just paint the concrete and call it finished, although applying plaster is basically the same thing, it just does not meet the definition of a finished space.
Now all of the realty legalize aside and talking practicality. In no way in Minnesota should you not drywall your basement. You should be insulating AT LEAST from ground level and up - especially around the edges (you can do this before it is finished). The framing also gives you an easy way to run electricity to outlets and lights.
There is just no reason to not frame the outer walls in the "finished" space. You do not want to subject whatever you are keeping down there to massive humidity and temp changes, you do not want it easier for bugs and rodents to get in and so on.
From a $$$ point of view if you painted your basement walls and left it like that your house would probably lose value, no matter the time, effort and quality. Anything done well out of normal standards like that is usually a red flag on the house.