If you had to ask Gramps or Gram this question, they would tell you that they never stole the tires from a senator’s car, but simply borrowed them. The protagonist’s grandparents have a knack of getting into trouble “as easily as a fly can land on a watermelon.”
With regard to the incident with the tires, their car had two flat “sprunkled” tires, and the easiest solution seemed to be to borrow the back tires from a nearby vehicle, which just happened to belong to the senator. By Gramps’s and Gram’s logic, since this type of loan is fully acceptable in Bybanks, Kentucky, it should be just as readily acceptable in Washington DC. In Bybanks, it would be assumed that whoever borrowed the tires would return them later, and Gram and Gramps assumed, incorrectly, that the owner of the tires they borrow in DC would know that their tires would soon be returned.
In a nutshell, the mistake that Gramps and Gram make with regard to the tire has two parts: firstly, they assume that the same rules applicable in Bybanks apply in Washington DC. Secondly, they inadvertently choose to “target” a vehicle owned by a senator.
This is not the only time that Gramps and Gram get into trouble over a misunderstanding. Sal also recounts an incident in which Gramps is pulled over for driving on the shoulder, which he had thought to be another lane.