That's correct. Obama never said it in public and no one ever said he said it in private. They only said he was going to do it, which was a fantasy in their mind, but which they might have believed. It's easy for simple people to think all Republicans agree on one set of positions and all Democrats actively take the opposite points of view. (That's probably how people get labeled RINO for disagreeing with the majority of Republicans on even one issue.)
This was before lying was so incredibly common in certain circles. Unless people repent, the next go-round people will outright lie and say that Biden *said* he was going to do this.