"No exact match found" when using People Picker in MOSS with Forms Authentication

This week I've been working with a customer to implement Forms Authentication for their MOSS site. Actually, it's mixed authentication since they'll have part via AD and part via a database. There are some great tutorials out there, but some people run into the problem I did - after modifying the web.config files, you have to add the user in the database to your SharePoint site. But when you enter the user into the People Picker, you get "No exact match found" and it won't let you continue.

What I found was that if I switched the Central Administration site to use the provider I set up, I got an "Unknown Error", which let me to think something bad was going on. Thinking through it more, I had in the back of my head that SharePoint would be accessing the database in the context of the current user, which is, of course, wrong. It access the database as the user you told SharePoint to use to access the database. So looking at that user, it didn't have access to my authentication database, and once I granted it access, everything worked like a charm!