As long as your mouth isn't actually touching the metal part of the fountain, I don't see a problem. The water pressure is going to force any bacteria that was in the pipe out within a few seconds. If a person is really worried about it, they could just bring an extra bottle from home, let the fountain run a while, then partially fill the bottle and drink from it.
Being in a small enclosed space with coughing people in the winter is probably far riskier than drinking from a public fountain. But then, my immune system works a little too well, so perhaps I'm not the best example of a typical response.