That's incorrect...if you deposit 1 million BTC in the bank and they operate on a 10% reserve policy, they can then lend up to 9 million additional BTC.  They would have claims of 10 million BTC in their customers' accounts and 1 million backing those claims (10%).  Of course they're not creating BTC out of thin air, they are actually only just updating an account balance (or they could issue their own "Debt Coins fractionally backed by BTC").

Interestingly, many countries have much lower than 10% reserve requirements, and some have no reserve requirements at all.  In a system that doesn't have FDIC like insurance, where banks are allowed to fail, a bank can be left to decide for themselves what level of reserves they maintain (but buyer beware).  A bank could conceivably make loans and issue a currency (account balances) without any backing at all.  They just have to convince people that it has some value in some way.  They could setup an exchange that trades their currency for something else of value and establish some level of support without any explicit reserve backing.  Over time, people could come to trust the value of that currency and the bank could gradually withdraw its support from the exchange.  As long as the bank didn't inflate the currency, it could continue to maintain value.  It's not that dissimilar to bitcoin except that you have to trust this central issuer.

They won't be able to get their money immediately, but a bank can easily prevent a bank run from being particularly disastrous. What they have to do is explain in advance what their bank run policy is and have sufficient assets of some kind (which can be loans) to cover the run in the long term.

For example, if the prevailing interest rate is 4%, they can have an "emergency run interest" of 9%. If there's a run on the bank, they declare an emergency and cover withdrawals with 9%, fixed-term notes. Sure, some people won't be too happy to have these notes instead of bitcoins, but their value will likely be a bit higher then the corresponding number of bitcoins, so they could likely sell them for a slight gain.

This assumes the bank isn't in danger of going out of business. This means the loans (or other bank assets) must still be sound. This can only cover a short-term liquidity run problem, not a long-term solvency crisis. (It wouldn't have helped with the bank failures we saw recently.)

However, a bank can easily cover a bank run with non-cash assets. This is another way commodities can be used to inflate the money supply. You might not trust a bank to keep only a 10% bitcoin reserve, but if they had a billion dollars worth of gold or also owned many stable businesses, you probably would. So a bank can leverage any other asset to allow them to put more bitcoins into circulation than they could otherwise.