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I can. Having a warm moist box in a public bathroom that doesn't blow air.
Both of those are qualities which discourage the majority of harmful bacteria from thriving. Besides that, if people are drying their hands, it implies they have washed them first. Being in a bathroom is really neither here nor there. Urine is (in healthy people) sterile, your genitalia are only lightly colonised with skin flora. In my job, as a microbiologist, it's more important that I wash my hands before I go for a piss than after.
Fecal contamination from flush aerosolisation would be the only thing there is to really worry about, but even that's not really concerning unless someone's had the shits. Most public bathrooms get cleaned far more regularly than a home bathroom.
People today are honestly far more germaphobic than is at all necessary.