This is a weirdly persistent myth, but no, that's not the case (think about it; what would happen if you had an open hot water tank? It would cool down very quickly, and you'd have horrendous humidity problems). _Cold_ water tanks used to be like that (sometimes still are), which I suspect is where the confusion comes from.
Hot water getting into the mains would be a concern anywhere; in particular, unless all equipment is in perfect working order, there's a legionnaires disease risk, but there are many other risks.