Season 4 Carter would have never have allowed the mission to happen in the first place.
She wouldn't go "I guess no one would know", she would have fought more against it.
1969 happened by mistake, she had no say and still nagged 10 times more than she did in Moebius, which they decided to go back. I just don't believe it. I could lighten up on the episode a little bit if it wasn't just a set up for a lame story and one liners.
But like I said at least the ending is awesome, so we have that.