So basically its a quintessential pro wrestling story line
I don't for one minute believe that these guys don't like each other I know its all fake. After the turn I bet they were gushing to each other how great it was. So why not just take it to another level. Its pro wrestling you need to have a level of suspension of your beliefs.
You blur the lines where people know its fake but they still ask themselves maybe just that part is real.
The problem is you're not blurring any lines. You're making up lies that are counter to a well known truth, and then trying to pretending it's real to push a story. All that does is break the fans immersion and drags you out of it. It kills the storyline.
Wrestling works best when you can let your self get sucked into it. When you let yourself believe it's real. Wrestling fans wilfully do this.
What your idea does is shatter that believe. I can't for one second believe in that storyline when I know for a fact that it isn't remotely true. It's goes from "this is an awesome feud, I'm really looking forward to it" to "this is stupid" instantly.
When you want to bring in some reality you need to bring in known truths. The fans will probably already know about it, and they can just keep going with it. It doesn't hit a 'no, that that's not right' reaction and jerk away your suspension of disbelieve.
Look at the Miz and Cena as a recent example. That was all about taking known truths and pushing them into storyline. Everyone knows that Cena doesn't want kids, that he didn't want to get married. That he's leaving WWE to do other things. They were truths that were added to storyline. They didn't make up some random lies.
Everyone knows it's fake, but when you mix in fake and lies you don't make anyone question anything. It's all lies. When you mix fake and truth then you can blur lines.