I was not even aware of this being used as a tactic. I only read the first page and the last page and a half, but it appears to me that the problem is that players invite a single player to the other side to ensure that no other teams that are scouting for open team games will join. Then the game gradually gets filled up with new players who sign up as individuals and are less likely to be part of a good team. Finally, the invite expires and a third player also joins as an individual. This seems like a really cheap tactic that can only really be used to ensure a low level of competition. If this fix is easily implemented, I support it fully.
I also don't see a problem if (for ease of implementation) it is linked to the scoreboard. If that means that a returning player has to finish a game before receiving invites, then that is a small price to pay. There are plenty of ways for those players to get into games during or before their first completed game without an "invitation."