I haven't looked into it too deeply, but I think I'm OK with regulation requiring a certain percentage be held as reserves. Without that regulation, banks were far more aggressive in their reserve levels, leading to greater numbers of bank failures when things took a turn.
I am NOT ok with a regulation requiring a 100% reserve requirement.
Finally, as was explained to Nimrod previously, it's not two people owning the _same_ money.
I suppose you could say that multiple people have a claim on the same _pool_ of money in the form of a demand claim upon request (and that pool is insufficient to satisfy all demands if everyone were to make a demand at the same time), but the cash is owned by the bank and only the bank until the withdraw is made (by either the depositors or by a borrower). And also note that this situation arises all by agreement between the bank and the depositors (and borrowers when they are part of the picture).
In its simplest description, you effectively have a group of people putting their money together into one pool (the depositors), agreeing to allow any depositor to make withdraws from the pool at any time they desire up to the amount they've contributed, and authorizing the bank, as the manager of the pool of money, to make low risk loans, reducing the pool of money below the total amount that can be withdrawn by the depositors. If the depositors agree to the situation, I see no reason for government to stick their nose into these people's business.