For the splitDAO() function to be properly executed, the contract must 'burn' DAO tokens in order to receive any amount of ETH in exchange based on the split ratio.
What part of the code or terms & conditions implies this 'must'?
Your argumentation basically boils down to this: the hard fork will be done because it can be done.
For me it looks like this: the Ethereum community is free to do whatever they want with their ledger, just as the outside world is free not to treat this ledger seriously any more.