Why, because of your imaginary 'put'?

If it is algorithmically guaranteed that you can convert 1:1 from a parent chain to a sidechain, then the fiat exchange rates for each can not diverge, aside from a small spread reflecting time preference (because it may take days to transfer between chains unless you use atomic swaps. But then market makers will happily offer atomic swaps for a spread).

I don't understand why you find this concept difficult. I think you are getting confused by Altcoins.