It's a good question. I'm sort of on the fence about that myself.

The most reasonable way to look at it is that Paddock was involved with child trafficking, and that if he were involve, undoubtedly the brother was, too. So perhaps the charge is a means to an end ... a truism in that he was in possession of CP, but that the arrest served a double purpose. The Paddocks don't look like the most dependable people on earth (understatement), so they could be afraid he'd talk .... or try to wring money out of them as blackmail (as if that was going to happen), or get a bigger cut, or move up into the position his brother held.

So all of the above, but my best guess is that the CP was real and that the Paddocks were dirty. It's why they were targeted and we can prove that statement true because of the wiretap the DEA took out on him. This was before anything in LV happened. Therefore, there was a loose end, they needed a false flag, and they got rid of Paddock (the loose end) and got their push for gun control.