Yes, the option to Log all account logins normally logs every single login to a website. What I assume is happening is this: ClassiPress is using one or more of the WordPress Login page Hooks, which are Actions and Filters that hook into WordPress Login page processing. BPS also hooks into these Login page hooks. ClassiPress is most likely calling the hooks before BPS hooks so ClassiPress will override the BPS call to these same Login page hooks.
Does ClassiPress have any sort of Login page options where you can control what happens on your Login page? Something like a turn on or off option/button? Or is this hard coded into the ClassiPress theme without giving you any control or options?