It is just that they choose to be listed on both exchanges. The company keeps track of the shares.
That's a decent guess but wrong.
All the ones listed on both exchanges are NOT dual listings. For many the underlying asset is actually not listed on either - and the listings on them are pass-throughs. So they're actually funds backed by shares of the underlying asset and shares in them are NOT shares in the underlying asset itself (the managers pass-through the benefits from the underlying asset).
There's NO share that's dual listed on both BTC.CO and Bitfunder (there's three that are listed on BTC.CO and have pass-throughs to them on Bitfunder). There's one I can think of that is dual-listed, but it's on BTC.CO and LTC-Global. Rest are either listed on MPEx, Listed on BTC.CO (with a pass-though on Bitfunder) or not listed anywhere (ASICMINER).
A pass-through is NOT the same as a dual-listing, as investors in pass-throughs have ZERO rights, entitlements or claims directly on the underlying asset. So, for example, if the manager of the pass-through vanishes you have zero rights to anything from the underlieing asset. And you may well have to pay a premium to buy in and only receive part of dividends.
ESECURITYSABTC is dual listed on BTCT.co and cryptostocks.com and on ltc-global, but I think they are the only exception. The rest are pass-throughs like you describe.