Guess what!!!! (I'm pretty excited about this.) I found out why Tim Hortons has no apostrophe!!!! There is a Real Reason!!!!**
Here's what my research has yielded. Sit down and listen.
The restaurant started out (in Ontario in the 1960s) as Tim Horton's. The apostrophe was dropped only when the chain expanded into Quebec (not sure when that was). In Quebec, by law, all business signage has to be translated into French, so Tim Horton's Donuts would become Les donuts de Tim Horton. Producing new signs for Quebec would be expensive, so the chain dropped the apostrophe and became Tim Hortons (pretending, you'll notice, that this somehow removes any hint of the possessive. By the letter of the law, maybe, but it doesn't change the semantics).
In English Canada, we complain about the missing apostrophe. In Quebec, no one is fooled. They know exactement what went down.
**I doubt the same can be said for Milestone's.