I've been on both ends of this....
I used to volunteer at dd1's preschool. Parents would bring kids in that seemed a little tired, but they would just say, "Oh, he/she stayed up late" or something like that. Twenty minutes later the "tired" kid would be vomiting and running a fever. When you asked them if they had been sick earlier they would say, "Yeah, I was sick all night. Mommy/Daddy gave me some medicine and said I would be okay."

Now THAT is super annoying... I can't even imagine making a kid who felt like that go out!
OTOH, once when my dd2 was in the hospital her Dr let us have a pass to go out (she wasn't contagious). We were 3 hours from home with no family or car, so we decided to walk 3-4 blocks to the mall. Dd2 wanted to go into the Crayola store to look around, and all of the sudden she barfed 4-5 times all over the floor. It was horrible!! We couldn't leave right away because I had to find a salesperson to notify about the mess on the floor, and then dd2 decided she needed a stuffed crayon, which I bought mainly because I was so mortified! I took her to the bathroom and cleaned her up for the walk back to the hospital. *sigh* She honestly didn't have anything anyone else could catch (and I had NO idea she would vomit), but of course a person just watching the episode wouldn't have known that. Luckily the saleslady was very kind and acted like it was no big deal. I have to agree with others here though about leaving. No way would I have just continued to browse around the store or mall while there was the possibility of getting sick again!