Whatever the player is doing, if he went to see the stats of the season (season 1, 2 or 3, it's not important), the screen stays visible. Even if he starts a queue, it's still visible in champion select, preventing the players to chose his runes/masteries or to comunicate with other players.
I've been able to remove the screen a few times by clicking on my Summoner Profile, but it doesn't always work.
1. Open your profile.
2. Click on Leagues.
3. On the down side of the screen, click on "see more stats".
4. Now, the screen that appears on the current server (last VI patch on NA by example) appears. The players can see his ranked stats.
5. Navigate into the client (start a game by example).
6. Notice that the page stays visible and it blocks your actions.