The way I'm reading the rule, I'm sure it's to designed prevent players from being on multiple teams together at the same level/division.
As an example ... you decide to join 4 teams in different areas with friends. This means, you are limited to one other person who can be on the same 4 teams as you.
So at most, one pair of players can be on 4 teams, which means either two single spots, or one doubles pair. This means that these two players won't determine the match entirely.
Now, imagine if more players were allowed to play on multiple teams at the same time? Then it would be like mercenaries, with the mercenaries playing the most tennis.