Does the auto attendant answer calls first, or does it a backup for a live person?
If there is no delayed ring being utilized, you could try splitting some of the POTs lines and connect a few single line telephones. If the issue is being caused by the CLEC, the single line phones will ghost ring along with the Partner phones.
If the Partner phones ring by themselves, then the problem is system related.
This may not apply to your situation, but here in Massachusetts, Verizon has 3-way calling enabled on many phone lines as a "pay per use" service.
Many times, shortly after a call has completed, the phone line will go active for a second or two. In some instances, telephones will ring, but nobody will be there.
Verizon has said, believe it or not, that the issue has to do with the 3-way calling feature resetting and the way to stop it is to have 3-way calling disabled.