I don't understand your objection. The coins that are valid on both sides of the fork have nothing to do with each other.
The point is that if you sign the transaction in one fork, the recipient can submit the same transaction to the main chain and also get your coin there.
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If I found myself at all tempted to use both forks, I think I'd create a set of addresses that I owned in both forks and send all my pre-fork coins to my own addresses to split them.
Example:
Pre-fork output for 10 BTC is sent to address 1AAAAA
Fork occurs
I create address 1BBBBBB and 1CCCCCC in both wallets.
I transmit a transaction to my BTC peers spending the 10 BTC output previously received at 1AAAAA and assigning 10BTC to address 1BBBBBB.
I transmit a transaction to my alt-coin peers spending the 10 BTC output previously received at 1AAAAA and assigning 10BTC to address 1CCCCCC.
Once both transactions have made it into their respective blockchains, I can now safely spend the 10 BTC in both networks without fear of the transaction being re-broadcast on the competing network.
If someone were to capture and re-broadcast either of my initital transactions to the competing netowrk, the coins would still be under my control, and I could re-attempt to move them using the same technique.