Hi Chipp, it's because the tire part has end caps on it which overlap each other, making for self-intersecting object. Any time you've got pieces of an object that run right over top of other pieces it will tend to confuse intersection calculations.

If you formed this by Flow you would want to leave off the end caps on your base object that you are deforming, to avoid generating these types of overlaps.

Here I've hidden the outer surface of the tire so the 2 internal end caps are exposed so you can better see what they are:






I've attached a repaired version of your tire that has those internal caps removed and then separated and rejoined and without the self intersecting areas and the boolean should work ok now.

- Michael

EDIT: Burr is beating me to the punch these days! :)