Currently, for reports submitted for toxicity, the logs are reviewed by the Instant Feedback System. It is a very thorough system that scans through the logs of every match that is reported within minutes of the reports being submitted. If the logs are found to have no toxicity, the reports are discarded as "false" reports. If the logs are found to contain toxicity, they are applied to that players account. In the case of a first punishment (the 10 game chat restriction), it generally takes more than one match for a player to accumulate enough reports to be punished. If the player is not typically toxic, and only display toxic behavior rarely, it may take quite a few matches before they are deemed worthy of a punishment by the IFS. Punishments are based more on a percentage of reported games, than on a set number of reports received. Note: This is only true for the minor toxicity cases; hate speech and threatening behaviors do often escalate punishments.
It is possible that if you were still playing, but hadn't logged out and tried to log back in, that you didn't see the pop-up with your Reform Card. All punishments issued by the Instant Feedback System for intentional feeding or toxicity are accompanied by a Reform Card, which is a giant pop-up that you have to click through to continue playing, and an email. It contains the chat logs of any recent games that you were reported in, which can be anywhere from 1-3 games, that you can copy with a link. The Reform Card is visible every time you log in during the course of your punishment, so if you have 10 games of chat restriction, then it should be visible each time you log in until those 10 games are finished. You can read about the Reform Cards here if you have any more questions about how to retrieve your logs from it.
If you try to log back in, and still cannot see the Reform Card, you can submit a ticket to Player Support asking them for the chat logs that would have been contained in your Reform Card. They will be more than happy to assist you. They also can help you any time you do not receive an email that should have been sent. Many times the emails from Riot can be accidentally placed in a spam/junk folder, or overlooked, but if you still do not see the email that should have accompanied your Reform Card, Support can tell you what it would have contained.
It sometimes helps players to see their logs, because they may not realize that they have been reported in more than one match. Odds are, if the only thing you said was that one line, you would not have been given a punishment. So, there may be some things from your logs that you aren't remembering, or that you aren't realizing are considered toxic by the Instant Feedback System.
One last note. There are some cases which are reviewed specifically by Riot staff, and are not punished through the IFS. Any of the manually issued punishments do not come with the standard Reform Card, to the best of my knowledge, but they are typically much more rare. It's not the sort of thing that generally happens for a typical chat restriction.
