Different users with same login credentials in different sites

I would like to use multisite to provide BBPress forums to my customers, where each customer would have its own BBPress forum, and they need to be perfectly separated.

More specifically, I would like that two people, related to two different customers, may use the same userid to connect to their dedicated BBPress forums.

For instance, “Homer Simpson” would login to blog1.mysite.com with login credentials “acme/acmepw”, and “Marge Simpson” would login to blog2.mysite.com with the same login credentials “acme/acmepw”.

I would like to know how to manage this with multisite, since through what I read in the documentation, it sounds like it is designed to share users between sites, and that’s exactly what I don’t want. But I also would like to avoid installing a WP instance for each customer, and that’s why I would like to be able to to it with multisite.