There's zero proof of that justification for the ridiculous law. If it were even slightly true, I'd expect to hit a significant increase in discarded cans and bottles the moment I cross the line into Ohio or Indiana. Instead, there's no difference.
Theoretically, one could make the case that Michiganders are such innate slobs that they are incapable of understanding the purpose of trash cans without the added incentive of a 10 cent per can deposit. Although tempting, the citizenry of Toledo or Ft Wayne are not noticeably different, and yet they manage to put their cans in the trash on a regular basis.
Overall, this is just another example of the failed regulatory mentality that has successfully driven Michigan into the ground.
It does cut down on litter though, I can't proof it scientifically but I know there are people who walk and bicycle around the rural roads looking for can and bottles on the side of the road and looking in trash cans to make a little bit of extra money. You don't see it on the interstate highways but you will see it on the other roads, etc.
I use to live in Michigan many years ago, I now live in a better state politically (Tennessee), and were I live you will find people going along the roads picking up the aluminum cans to sell them for scrap aluminum.