Last I checked the Apple software did not setup VERIZON mail correctly if you Specified AOL I recommend still using Verizon setup, which usually works. Double check pop id is email@example.com and other settings match the settings at
I was able to do it a couple times (on my computer and a friends) but since I reinstall OSX, I have been unable to do it again. What I did was ... created a new mail account using a real AOL email address. I had one but if you don't just create a one. Once I did that, I simply went into the settings and changed everything to my verizon email address. Like I said, I have not been able to repeat what I did before because it won't let me change the username (gray out). It wasn't grayed out last time.