Consider also that 'owners of the currency' have a financial incentive to mine below-market rates to protect their investment and ensure their transactions get processed.    So the cost to produce hash power would probably be greater than the direct payout received for mining it.

I suppose a rich, private company may attempt to undermine the currency and earn their profits on the side rather than directly via double-spending.

Conclusion: don't rely solely on proof of work to define the best chain.  If someone pops up with a new chain that is more than 6 to 10 blocks forked they are ignored until manual intervention is taken after community consensus can be reached about whether or not that 6-block fork was mined in private or the result of a legitimate chain split caused by a network outage.