My read of the situation: SBF's comments were about assets (balance sheet) rather than FTX's liquidity. I believe SBF was saying (paraphrasing) "Our balance sheet is fine; FTX doesn't invest customer assets; we're processing withdrawals as fast as possible." That's different than saying "we have 100% liquidity."

Banks make similar statements all the time -- they require regular audits of assets (stress tests) and maintain some minimum levels of liquidity.

Banks say that they don't invest deposits?

In the Glass-Steagall sense, they probably shouldn't. Mixing commercial banking and investment banking was illegal from 1933-1999, and it is (arguably) one of the underlying factors in the 2008 financial crisis.

Note: There's a difference between being a custodian of customers' investments (brokerage / commercial banking) versus proactively investing customer deposits (investment banking).

Going to need a _huge_ source on that claim. Investing customer funds is the primary way banks make their money, and has been that way essentially since the invention of banking.

From https://en.wikipedia.org/wiki/Fractional-reserve_banking:

"Fractional-reserve banking predates the existence of governmental monetary authorities"

Banks lend deposits. That's how they make their money. They have to keep some part of the deposits as a reserve.

Real regulated banks have access to the Fed to borrow in a case of a bank run.

And FDIC to de-risk customers from feeling they need to do a bank run.

To a large extent, but not completely.

Anyone who has more than the insured amount, or anyone who needs their money in the near future will still engage in a run.

There were several runs during the 2008 crisis, the most famous is the run on IndyMac Bank.

https://en.wikipedia.org/wiki/IndyMac

It’s pretty clear now it a last ditch Hail Mary effort to save them from a bank run that would ruin them