The exchanges agreed to hold custody of your BTC and your BTC only. Any forks that may occur are a different matter
I don't think this argument should hold much to water your position, although you made and had a soft landing of your post in the end. Thus, talking about forking and holding of the coin itself, I think it depends on the exchange because I noticed that certain exchanges especially, coinexchange does release fork coins.
Also, I think that should even be the case naturally, that exchanges should also have it as a duty to deal with the properties of the coin as if it were the coin directly; that is ,every proceeds of the coin accruing from the coin.
obviously, this depends on jurisdiction. but when it comes to the courts, usually we're looking for what's reasonable. so let's think about that:
i could generate a million forks of BTC right now (that nobody uses, of course). is it reasonable to assume that an exchange is obligated to download all my million forked clients and send me my forked coins?
of course not!
so i think it has to boil down to whether there is actual demand for a fork, and whether the fork is even active at all. either way, i'd be very curious to see arguments heard and court decision issued where the exchange explicitly says in its terms that it won't pay out forked coins.