The buddypress registration form is somehow overriding the registration form that's generated by Theme My Login at /register. That happens whenever I associate /register with the bp registration page, at network admin > settings > buddypress > pages. The only way to have the TML registration form to be displayed is if I don't have any page associated as the bp registration page, which isn't an option, as my users wouldn't be able to use all the parts of my site that need bp and bbpress if they've registered through the TML form.
I've searched the internet for a solution on this, but so far didn't find any. Michelle Schull told me it wouldn't cause me any issues to use TML for the login part and buddypress for registration, so if there's no way to associate the TML registration form with bp, I'll do just that, but I obviously would like to see if I ca get a solution first.