How has the ETC/ETH hardfork not collapsed, how have they made transactions incompatible?

Firstly I'll be the first to say this may not seem like bitcoin, but hear me out... this is to learn from the hardfork problem AND does require bitcoin as a store of value when extracting the funds...Person 'B' has 100 ether recognised in both ETH and ETC because they are not associated with the DAO. (Assumption, is this fair to say that the transaction is recognised on both networks? If not, how?)If B now sends some ether to address C but also includes some coins returned from the DAO hack, ETC will block this transaction but ETH will pick it up and as allowed.So now we have this weird effect where B and C have funds in ETC and ETH respectively.I would have thought this meant that if person B actually owns address C they can simply visit an exchange and withdraw his ETH for bitcoin and buy new ETC (which is compatible with ETH) to repeat the process thereby stealing all the money?I'd really like to understand if ethereum does something bitcoin doesn't that protects from this attack? via /r/Bitcoin http://bit.ly/2aCzQiW