This is not true. If this were true then false reports wouldn't pop up a warning on your end like they do now.
The timing of the pop up is in line with what Riot has said about prompt feedback. As such, it has nothing to do with false reports being counted or not.
The pop up is a warning that you've been reported a lot recently. It takes next to no processing time from the servers to figure it out, so the warning can come immediately. If you've been acting out, you change. If not, you ignore it. Either way, you queue up for the next game.
Meanwhile, the Server goes and processes your chat log for that game. It has to run that game through whatever language processing Riot has and evaluate it. This can take several minutes, by which point you're likely in another game. If Riot showed you the warning after they had confirmed an offense, it wouldn't be for the game you were just leaving, resulting in a false sense of what you did wrong, so they stick with the two phase system.
We know that the server doesn't process things instantly because of the feedback for the player doing the reporting, which often comes a few minutes after the game ended. If Riot didn't discount false reports, then the feedback for the reporter would be almost instantaneous.