It’s not a lie.
Certainly for up to $250,000 deposited at an FDIC insured institution, it is absolutely true that you can assume that you have cash deposited and available. If at any time the bank gets itself into a position where they can’t make good on that, FDIC will fix it so you still have your cash.
That is precisely the mechanism that the federal Government makes available that gives you a place to park your cash.