I can assure you that what I describe IS how real world banks work. You can look at the balance sheet of any retail bank and it will spell this out clearly. I've worked in retail banks and have some hands one grasp of their day to day operations.
Your confusion is a common one - you mistake the process that results in the creation of M2 money with the day-to-day operations of retail banking.
Modern retail banking is a very simple business - they borrow funds (from depositors, other banks, sometimes central banks, commercial loans, etc.) and then lend out the SAME funds while keeping some back in liquid assets (cash, deposits in central banks, short term government notes, etc.) in reserve. The trick is to charge more interest on what you lend out than you pay on what you borrow while managing the risk and cash flows involved when you have a mixture of terms (expiries) of borrowings and lendings.
I think I've given a reasonable summary in my posts of how banks work. I've studied the balance sheets of retail banks and have been exposed to their day to day operations so please don't simply disagree with me and point me to a document on M2 money creation - if you think I've stated something untrue, then highlight it and describe where I'm wrong.