No, I used the on-site search, and missed that page. It says that FRB with Bitcoin is possible, which contradicts what you are saying. The page also makes an error in argument. It is not necessary that other people accept bitcoin substitutes (like checks). What is necessary is that depositors accept that their deposits aren't matched one-to-one.
Back to my example. I deposit 10 BTC in FIBB. FIBB then lends you 9 BTC. You've got 9 real BTC, so you don't have to worry about whether anybody else will accept, say, a check denominated in BTC. I've got 10 BTC, it says so right here in my bank book. I can't get it all back instantly, but this is presumably money I'd not be using immediately.
How this works is that, after some period, you're supposed to pay FIBB 10 BTC, as principle and interest, and FIBB splits that with me, so that I've got 10.5 BTC in my account, so I get interest. I forgo the use of my BTC for a period, and I get more BTC back. I may or may not be able to do better by investing elsewhere, but (assuming I trust FIBB) this is a safe and guaranteed return. There is some risk: FIBB loses if you don't pay it back, and I lose if FIBB has a catastrophic failure. Your risk is what FIBB will do to you (sue you, make it harder for you to ever get a loan again, whatever) if you default.
This is how banks used to work. (They also used to have a role in safeguarding money, much less important with Bitcoin.) They operated that way for centuries, without any sort of government guarantee. Banks did fail, taking their depositors' money with them, but not often enough to discourage the others.