I thought PSA changed their policy about this. Here is a screen shot from their fee schedule page. Look at the bottom line. It notes that one must be a Collectors Club Member to use Bulk Services. It doesn't say that about the other services, so one would have to assume that you do not need to be a member to submit at the other service levels. Otherwise, why only note it about the Bulk Services?
Edited to add: I could be wrong. I haven't submitted anything to PSA in a few years. However, I thought I remember reading that change on the PSA message boards.