It sure does sound as if the on-line system thinks you're an SSSS candidate while the kiosks don't.

Have you updated your profile with your full name for TSA Secure Flight ? This could be different from you ticketing name (ie: Joe W Smith) as your full name is required (ie: Joseph William Smith)
Sign in on the home page then: View Account Details->Manage Profile->Traveler ID(s)

This TSA requirement is new. I think it started Jan01 tho airlines have been trying to collect the full name for months. One goal of it is to reduce the "false" matches due to similar names.
But if this is your problem, since it's new I'd think the CO reps would be fully aware. Perhaps your "ticketing" name is a close match to a name on a TSA watch list. That could explain why it's not common but still seems odd why the kiosks work ok.

Good Luck resolving this odd one !
Steve