On my Verizon Galaxy Note 2, T-Mobile prepaid cards works fine, but AT&T prepaid card does not?

[BuyOneGetFour]

I don't think I can get more confused about my Verizon Galaxy Note 2's ability to use GSM SIM cards on other carriers.
Not too long ago, I was NOT able to use ANY prepaid cards from GSM carriers in Europe while over there.

This morning, I picked up a couple of prepaid GSM SIM cards. One from the local AT&T store and one ordered from
T-Mobile's website(during their $0.00 sale).

First, I plugged the AT&T prepaid in to my Note 2. This card had already been activated on a prepaid AT&T GoPhone
and works fine in my other plain vanilla unlocked GSM phones. It does NOT work in my Note 2. It just kept giving me
the non-Verizon GSM card error message.

Next, I tried the T-Mobile card. It was activated in an unlocked GSM phone and worked fine for incoming/outgoing
calls, as well as data. (put it on a 3-dollar-per-day plan) My Verizon Note 2 worked fine. Voice calls only. Data
wouldn't connect.

Seeing the T-Mobile card worked fine, I took it out and plugged the AT&T card back in. Still nothing... just the
non-Veriozn error message again as soon as I turned the phone on.

Can anyone tell me what's going on here?

Thanks!