From the FAQ:

So, what’s the deal... are you really a bank?

We are not a bank. We work with partner banks (soon to be announced) to provide FDIC insured products. What this means for you is that your money is safely insured with our partners. Our wholesale partners provide the financial products, we provide the customer service and experience.

I'd say the problem is how different parties conceive of the word "bank". When you're a consumer, the word "bank" means the entity that you interact with to do your banking. At the same time, the legal definition of "bank" is something entirely different, requiring compliance with many more laws than what BankSimple is doing. So, as far as I can see from the point of view of a customer of BankSimple, they will be "my bank" because you interact with them and not with the banks that are actually responsible for the safekeeping of your money while it's in your account.