You were told correctly. Oklahoma accepts any valid permit from any other state as their own, and in addition, recognizes ID from Alaska, Arizona, Vermont, and Wyoming, since those states don't require a permit.
Our law after Nov 1 will allow any licensed person to carry "concealed or unconcealed".
The only caveat is that if you are no longer a resident of the state where you got your license, that license may or may not remain valid, depending on the rules of the issuing state. However, I'm pretty sure that being active duty military here in Oklahoma means that you are lawfully still a resident of your home state.
I'm not a lawyer, BTW.