PokéCommunity, from my experience, is an independent site, yes.
However, if you're looking at rivalry, from my experiences, Bulbagarden and Serebii have some sort of unsaid feud against each other. Although for all I know, it could be just in jest. But Bulbagarden and PC? No way.
In my experience, at least, the thing about "15 infractions making a permaban" seems to make a few people uneasy. (It would definitely make me uneasy. I have a habit of accruing trivial infractions, and I had about 10 or so in one year at Bulbagarden because I kept doing small things.)
That's Bulbagarden's staff, though. PC's tends to be a little bit more laid-back to the point where most of them would rather just explain things to you instead of handing those out like candy, so if you
do get that many infractions, you
really screwed up somewhere along the line. In all my time on PC and after pulling quite a lot of crap, I've only gotten one infraction, and that was reversed after some discussion. Besides that? Nothing but stern talkings-to now and then.
Just remember that a difference in rules doesn't necessarily mean one community is harder to get along in than another. It all depends on the mods enforcing them, really.