Yes, that is the rule and everything that anyone has said otherwise is incorrect.
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It was a horse collar tackle. It was actually a fairly textbook example
with the difference being that Daniels' athleticism in not going down immediately and the speed and momentum of both players carried them both forward and then 90 degrees to their right as the tackle was being made, and finally sent Daniels rolling toward the endzone.
This is NOT to say that he was "slung" down horizontally or sideways. He was pulled abruptly straight backwards to his back on the ground by the nameplate area of his jersey. It happened like this.
The Bama tackler grabbed Daniels with both hands by the nameplate area of the jersey (condition 1 of 2) and pulled abruptly (condition 2 of 2). As the result of Daniels' strength, speed, and momentum, this did not immediately pull him to the ground but jerked him around and they both spun such that they were facing the sideline as opposed to the goal line. The Bama tackler now pulled forcefully again (or in continuation) pulling Daniels by the nameplate area
directly backward -- exactly in the manner of the "classic" horse collar -- taking Daniels all the way to the ground. Full stop.
The second tackler momentarily interrupted the abrupt backward fall (together with their momentum) but Daniels hit the ground from the horse collar landing on his back. The people who wish to see Daniels pulled by the designated area abruptly to his back can see it right there.
But again momentum sent Daniels rolling toward the goal line, after he had been pulled flat onto his back and his athleticism, along with a friendly teammate's tug set him upright. One shouldn't be distracted from the essentials by this conclusion.
This is all easy to see at slow speed or simply by toggling the play and pause button on the clip in the tweet. There is no reason the replay booth and the network both should have missed this since they both have the ability to slow and pause and replay until all is clear. I could do it on an iphone.
I made some stills but I am tired. Look at it for yourself and I think you'll see. iirc the moment where you can pause when they are sideways to see to classic horse-collar abrupt backwards pull of Daniels to flat on his back is at 2 seconds on the tweet.