The "freaking out" is, I assume something along these lines:
We were all taught in high school history class that the Great Depression was caused by fractional reserve banking, and that's why, boys and girls, today we have the FDIC which requires a 10% cash reserve.
So, it kind of makes sense: in the middle of a financial crisis, the feds quietly remove the requirement for a 10% reserve, which should, on its own, undermine confidence in the banking system; and no one notices or cares. It's like they didn't remember high-school history or something.
I freaked out a little too, I must say.
However, I will point out that the FDIC is still there, still insuring deposits for $250k, still holding an enormous reserve of its own, and still allegedly backed by the Fed's ability to send over a truck full of money as fast as the ink can dry. There is no danger of 30's-era bank runs. The real danger is from that truck full of money sucking the value out of your deposits.
Solution: don't keep too much of your wealth in cash.
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As for the much-debated link between inflation and stock prices:
Stock prices generally respond positively to inflation -- just like everything else. If the price of a loaf of bread doubles every day, then the price of Apple will increase, and for the same reason. It doesn't matter what it's officially "denominated in", if you are personally valuing it using an inflating currency, then it will seem (to you) to rise in value.
I think that the fallacy is to think that Apple is some kind of pile of money, that loses value as more dollars are printed. Apple is not a pile of money. Apple is a machine that takes plastic and silicon and turns it into something useful. Even if the government declares pine needles to be legal tender, Apple will still be a machine that makes wealth, and you can still be wealthy if you own it.
Obviously, inflation is going to change consumer spending habits, credit, and efficiency, in ways that might damage the economy, and Apple in particular. This is a separate effect.