Gene considers that perhaps Finny has been broken because he broke the rules in chapter 6. Is this a valid consideration?

No, not really. I've always felt that this was Gene's way of making excuses for something he carried a lot of guilt about. Finny of course fell because the boys were fooling around. All of them were fooling around, all of them were breaking the rules, and although Gene did shake the branch..... the entire accident was not solely his fault.

After Finny falls, Gene carries guilt, but also looks for ways to excuse himself and blame Finny. Soon, everything Gene does turns into penance and Finny takes advantage. I would say it turns into a strange friendship, but the two never really can be considered friends.