They hand you your coffee at boardwalk? They make it for you? How is this set up? At Pop, its a food court. The beverage stations are on an island on the seating side of the check-out lines. You fill your own mug with whatever you want. My kids like to mix soda flavors. I mixed some hot cocoa (which they don't have at Deluxe resort refills) into my coffee and it was extra yummy. People also refill old and out of date mugs. I'm not passing judgement on those people, I'm just saying they do it. I've NEVER seen anyone get busted. Now, at Saratoga Springs, which is DVC, the refill station is in the cafe, which is not food court like. Its next to the check out. There are far fewer beverages to choose from too. There are also beverage stations at the pools at SSR and GF, but they're next to the bar tender, so he can see what you're doing.. not that he's necessarily watching.. but he could. Pop doesn't have beverage stations at the pools and also doesn't have food at the pools like they do deluxe. Maybe because the pool is so close to the food court. But Petals Pool Bar has the same drink menu as Saratoga and Grand Floridian. That said.. whether or not you bring your mug, if you fill a disposable coffee cup at the station, nobody is likely to even notice. You're entitled to the refill as long as you have/have paid for the mug. If you'd be more comfortable, keep the mug receipt in your pocket or purse!
Yes, I did use my Cricut.
If they think the CM is going to get germs from the mug, then certainly gloves are an option. The bakery workers wear them anyways. I wonder why Boardwalk would be different than the other deluxes? I refilled at Beach Club on my way to Beaches & Cream, and I didn't have to hand it to anybody. 
