If you had no choice but to hit the brakes then I don't see this as being your fault. When you do a group ride you assume the risks of crashing, that's just how it works. It is his responsility to fix his bike, your responsibility to replace your shoe.
Now, if you would have slammed on your brakes and swerved for no reason, I would have been pissed at you. Doing what you had to do, that's just riding.
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I may be fat but I'm slow enough to make up for it.