Is my Verizon Note 2 really unlocked whitout needing Verizon to unlock it?

[Windows Central Question]

The phone does work in the GSM mode on T-Mobile and receives H+ but is unable to get the T-Mobile 4G LTE even though the LTE signal is available. It also does not make phone calls when the only service is a high speed wireless Internet connection. Also the Internet pages stop responding after about 1 minute.