Why is it when people report falsely they don't get banned automatically?
Because there's not really any good reason to punish someone just on account of false reports. False reports do not result in punishments outside of exceptionally rare edge-cases, as the IFS can easily determine whether or not a report has merit through the review process that the report triggers.
Besides that, let's assume for a moment that it was a punishable offense to report players incorrectly. Someone happens to find someone who appears, by all rights, to be trolling, but, knowing that such behavior usually is difficult to catch, they might be opening themselves up to punishment if the IFS doesn't find that behavior to be within punishable bounds.
Y'know what happens then? The player doesn't report the troll, not because they doubt whether or not the player actually was trolling, but because they're afraid of getting punished themselves.
That's not a productive system.
Also, screenshots can be altered and a lot of the time when people post to public forums about others, it is falsified and doctored.
Well, there are really only two places that players can theoretically post doctored screenshots; there's the Boards, wherein their post will get removed due to Naming & Shaming (and even if that rule wasn't in place, a fake screenshot being posted to the community wouldn't get them anywhere), and through a Support Ticket report, which also wouldn't prove very useful, since Riot has access to the full, unedited logs of every in-client, in-game interaction, so they could easily check to see if the logs match the screenshot and...Boom. Nothing happens.
