If they are not breaking any rules, or the accuser lies, it won't matter if they are reported. The report is false and it will be thrown out by the IFS.
But as a general rule, if a player is getting in an argument with another teammate that lasts more than a few lines, and degrades into any form of personalized insults, even if their position in the argument is correct, they are breaking the rules of the game. They've moved into verbal abuse, and they are creating a hostile, negative environment where the other players in the match have to suffer for the actions of both parties involved in the argument. And at that time, if someone happens to say "just mute them and report them after" it should be a pretty clear warning to that player that they are doing something that they are going to end up being reviewed for.
The community tells Riot what they want punished. Riot usually listens. The ultimate decisions are up to Riot alone though. Therefore, Riot should inform the players when they are breaking the rules that Riot enforces.
This isn't entirely correct. The IFS was designed and implemented by Riot, but it's a learning system. A type of AI that was created to monitor the actions that the players in each region find inappropriate and punish the players who take those actions; ranging from various verbal filters to the FeederBuster module. With regards to many things, the decision for it to be punishable was made by the players, seen in the overwhelmingly high number of reports submitted. If the community decided today that it wanted to pick a random word and turn it into a bannable offense, it could, simply by having everyone mass report anyone who used it. Within a short period of time, the system would register that the playerbase finds the word offensive, and would begin to punish for it.
Of course, as you say, Riot has the ultimate decision making authority, and can at anytime reprogram parts of the IFS, or override any punishments that were issued. But they designed the IFS under the same principles of player input that the old Tribunal had. It simply doesn't seem quite as apparent, since we don't get to sit down with a bowl of popcorn and read the entire chat log anymore.