Travel Mugs and Timmy's

I brought my travel mug to Tim Horton's the other day and was told they couldn't mix the coffee in my mug for contamination reasons; they had to use one of their cups and pour it into mine. I understand that. I also wonder, do they always use the same cup or do they use a new one each time someone comes in with a mug? I think I'll ask the next time I'm there. If it's the latter, wouldn't that defeat the purpose of bringing in a reusable mug in the first place?