a popular bot wouldn't be tracking chat logs without permission or the user being aware about it/accepting to an agreement for it. there's a whole ton a legal stuff behind tracking chat logs that i doubt the notsobot developer would want to deal with.
at most, notsobot tracks and displays publicly available info about you; which is this.

if you're still paranoid, you can keep the bot inside a separate channel and for every other channel disable the bot from viewing it. ideally, this means the bot can only record information said on that bot channel, which is most likely just commands for that bot.