Are you talking about drinking from a bubbler? It's certainly possible to pick up some infections from common use items. Usually it is from contact with the object then touching the eyes or mouth though, rather than from the water. Because you aren't actually sharing the water. If it's something which concerns you then you really need to teach your kids not to use the bubbler at all because you don't know who touched it before you got to the park. And you also need to tell them not to touch any of the playground equipment as that is just as likely to be a source of infection. As is every door handle, bannister, shopping trolley etc etc which you touch throughout the day.
My advice, if you have typically healthy children, don't worry about it. Wash your hands when you get home. Or use wipes at the park before eating.
Mother of two spectacular girls, born mid-2010 and late 2012