The key language in the Minnesota DWI statute is "physical control of a motor vehicle." The Court held that a jury could, based on the totality of the circumstances, conclude that Mr. Fleck "was in a position to exercise dominion or control over the vehicle..."
The Minnesota DWI statute doesn't make a distinction between public and private places, making it a crime to "drive, operate or be in physical control of any motor vehicle...within [Minnesota]...under the influence of alcohol."
The Texas DWI statute, on the other hand, makes it illegal to operate a motor vehicle in a public place while intoxicated. Had Mr. Fleck been in the Lone Star State after his little bender, he may have been able to argue that the parking lot of the apartment complex was not a public place. Key to that argument would be whether or not the general public had access to the parking lot. Was the parking lot gated? Did visitors have to check in before entering?
Mr. Fleck could also have argued that there was no evidence of operation since the keys weren't in the ignition, the engine wasn't running and there was no evidence of the last time the car had been driven.