Q: Visual Voicemail - Cannot delete voicemails

I've not been able to delete my voicemails using the visual voicemail interface.

Initially, I was stuck on the Deleted Messages screen as the Clear All button was always greyed out. I saw a post that someone made in the forum here and found that if you access one of the voicemails in the Deleted Messages, the Clear All button would activate. I tried that and it works like a charm EXCEPT, 20-30 minutes later, the voicemails that I just Cleared, come back as saved messages and are sometimes even marked as New/Unheard. This is very frustrating.

I called AT&T and they were VERY quick to point out that this is an Apple iOS 7 problem. Is that true? Any suggestions?