Is this really the oath of the three-eyed crow?

Potential Spoilers Below

"Night gathers, and now my watch begins. It shall not end until my death. I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory. I shall live and die at my post. I am the sword in the darkness. I am the watcher on the walls. I am the shield that guards the realms of men. I pledge my life and honor to the Night's Watch, for this night and all the nights to come."

―The Night's Watch oath

It seems to me it fits the true purpose of the 3EC.

I think that men probably witness Bran taking this oath thousands of years ago when he went back in time and they initially passed it along in remembrance.  Then it got twisted to what it is today.  It would then be logical to think that since I think that Jon Snow will have to replace Bran as he is now old and dying that he will have to say the words again but this time to become the next 3EC.

Comments encouraged.  Love to hear the idea’s of others.  Most believe that since I present my idea’s as “fact like” I’m not open to change my viewpoints which is far from the truth.  I simply look at the information presented and go from there.  If you can shine a light on another way of thinking that opens the door to debate.