Haha I am not going to read through all my bank terms again but I doubt they have a disclaimer about fractional reserve banking, like "oh yea and if you try to withdraw your money at the same time as everyone else then we can't give you your money, sorry". But yea if we sign a contract actually saying this then they can do it as they want.
Scanning my bank's agreement, this is all I found:
If you have an Interest Checking account, Money Market Account, Online Savings Account, or IRA
Online Savings Account, as required by federal regulations, we retain the right to require you to
provide us with seven (7) days written notice before withdrawing funds.
I think the reason that it's not clearly outlined is that unlike an investment account, you are the legal owner of the deposit. If you buy stocks or something, you have a right to the stock, but not the original deposit. With a bank account, they are legally required to repay you the money on request subject to terms such as the one above.
Still, it's a well known business model, and it's possible to keep most of your money in cash. Banks offer free checking, so you aren't obligated to store lot's of money. You can use your bank just to cash checks if you want.
And really a lot of business models break down under the stress of everyone demanding what they are owed at once. Imagine everyone having a car accident at once. Insurance companies would have an issue.
My point is that banks aren't lying and saying "we hold all of your deposits in a cash vault and pay you interest just because we like you" they are holding your money because they can profit from it, and it's a mutually beneficial relationship in all but exceptional circumstances.