Huh, it never would have occurred to me to see that as inappropriate. If my coworkers are sick, I want them using tissues rather than spreading their germs around.
It's inappropriate because they are my personal property. The company did not provide tissues to employees. They were partially behind my monitor, so that person went out of their way to find them and use them. Combined with their arrogant taking of them with me present, yes, I'd say I had every right to be cross.
I don't want sick people in my cube. If they came in while sick last week, they've certainly had time to buy their own tissues.