You can trust strangers at the baths with your secrets precisely because they are strangers. They don't know who you are, and don't care. Your secrets are safe in the custody of someone who doesn't know what to do with them. Peter is not just a good businessman, he's a community leader, and so he has made sure that his bathhouse is the kind of place that can help guys out with both problems. They still don't want to be seen going into the baths.
Discretion is mandatory.
Most bathhouses have blocked off all windows and there are no signs or other exterior indicators of what they are. You enter through a dimly lit side door and walk up the concrete stairs. For many first-timers, the walk up those stairs is like the fearful exhilaration of approaching the top of a roller coaster. The final barrier to the plunge is the check-in. You will find a nice man behind a window with security bars.