There is no reason why fractional reserve banking could not be done with bitcoins. After all, it existed when the U.S. was on the Gold Standard.
It can't be done with bitcoin, because you cannot produce more bitcoins like you can dollar bills...And when the banks have to fufill the loan, they will have to send actual bitcoins to fund the loan....
Person A deposits 100 BTC. The bank A loans 90 BTC to person B.
Person B deposits 90 BTC. The bank B loans 81 BTC to person C.
Person C deposits 81 BTC. The bank C loans 72 BTC to person D.
Person D deposits 72 BTC. ...
Total apparent number of bitcoins in the system: 1000
That's classic fractional reserve banking and it works with dollars, bitcoins, gold, or seashells.
I think he's saying that the "apparent" number of BTC isn't the same as the "real" number of BTC because BTC isn't a claimcheck on something unprintable, but is itself unprintable. I.e, the fractional reserve isn't built into the currency itself. Sure, I can deposit 100 BTC and the bank loan 90 BTC of it out, but I can't spend that 100 BTC unless the 90 BTC is repaid, or unless someone else deposited another 90 BTC and I requested my withdraw before the bank could lend it out.
This is also true with fiat banking. As long as people do not withdraw their funds in mass fractional reserves works great. When there are bank runs then depositors will stand to take losses, what prevents bank runs is deposit insurance that protects depositors in the event that a bank becomes insolvent.
Actually it isn't, at least not in the US System. Recall that the USD is backed by the "full faith and credit of the US Government."
Now visit this link:
http://fdic.gov/deposit/deposits/brochures/deposit_insurance_at_a_glance-english.html"Deposits at ... insured banks ... [are] backed by the full faith and credit of the United States government."
In other words, deposits and the currency itself are backed by the same entity in the exact same manner, making them equivalent. Now I guess theoretically deposits greater than $250k or $500k in a single financial institution wouldn't have this quality, but to be honest, not many people have that much in a single account, people with that much money tend to have multiple accounts, and even if they did, the USG basically has set a precedent of never letting commercial banks fail for any reason, so the limit may as well not be there. They keep on increasing it anyway, the moment there's any sign of a bank coming close to failing.