I too would be interested in know if there are legitimate BitCoin banks out there. I suspect not for 2 ½ reasons.
First, I don't think anybody is audacious enough to do that. At the very least it implies one has a solid back office. It also implies that one has a government issued charter (with the regulation, fees, and oversight that goes with that). If a loan goes south, how do I collect? These are not unsolvable issues. I suspect that some of the ponzi sachems out there that promised a fat return or interest rates pretended to have some type of fractional reserve going.
Second, you can break banking down into 2 parts. One is the “cash handling” aspect. I have a negative opinion on BitCoin but this it does well. The second part, the fractional banking part, is to allocate capital by transmuting short term deposits into long term loans. I have a hard time imagining anybody needing a long term loan in BitCoins. Because the price is volatile, we would need to find a business that needed a big upfront loan in BitCoins for capital and was expecting to do business in BitCoins for the future.
Which takes me to my ½ reason. BitCoin users tend to be hard money types who hate loans. While I look aghast at the amount of leverage in the current system, I do think some lending (or to be more precise, some time aspect of investment) is necessary. I personally don't think BitCoin will be a real currency until we start seeing loans being made.