My view is this:

There is no such thing as privacy in a public place except for the right to keep your daks zipped up of course. Where can you go in real life without being filmed or asked for ID? There's not many places, that's for sure unless you plan on going into the outback and staying there. Large companies even record your conversations with their representatives these days "for quality assurance purposes" which we all know is a load of BS but that is their claim at any rate. The Internet is really no different but I believe that there's really no time for the bot owners you mention to routinely scrutinise log files just as a local council wouldn't have the money to spend on security officers reviewing every tape they make of shopping centres and beaches. Unless a crime or some other IRC related offence has been committed then the content in logs is more or less meaningless. Anyway, there's every chance that everyone in a room is going to be logging the chat - what they log will be the same as what the bots log and they can all do what they like with the logs, posting them on their websites, etc, if that happened to appeal to them.