Incorrect, so false. Similarly, if you believe "Nazarene" is the only right faith, it doesn't mean you particularly are a Christian, just that you rightly or wrongly believe something. I'd suspect you are aiming at something more substantial, but the question doesn't address, I think, what you were aiming at. I think perhaps, you were aiming at the idea of whether an understanding of one's salvation must be accompanied by the idea that is irrevocable or such.
I'd suggest you can be saved and mistakenly believe you can 'fall' out of God's hands. Fear, or a number of other wrong ideas, can give you a mistaken idea BUT that, itself, doesn't remove you from God's hand. It simply means you are needlessly fretting over something that isn't in your control.
( I'm monergistic, and it steers my understandings and comments)