If McDonald were selling 3rd party stuff yes, your example is flawed from the beginning.
If I brought in Grey Poupon to a Mcdonald's and they didn't let me put it on a Big Mac would that be what we are talking about? How does Wendy's come into play? What if I bought a Whopper and then subsequently a Big Mac and put the secret sauce from the Big Mac on the whopper?
If it stained the seats in my Porsche could I take it to any car wash?