Washing hands and physical distancing are still very much recommended (whether or not you also wear a mask).
Evidence for various properties of non-medical face coverings isn't that good, but the expectation was always that It might reduce spread a bit from someone that's infected (but presumably doesn't know it yet).
I'm not sure how we'd get particularly good evidence on that kind of effect (positive or negative). It seems plausible to me, and it seems plausible that it would also help reduce spread of other respiratory infections so I'm inclined to assume it's true or at least give it a pass.
Early on I think there was a significant risk that encouraging people to wear face coverings would take PPE from people who really do need them (and who can use them correctly), and that was confused with some ideas of how wearing face coverings might actually be risky for the general public. I suspect those extra things were largely made up to support the real reason (lack of PPE).
Regardless, it's interesting and reassuring that some of these things are being tested and not found to be true. (Though that's admittedly a bit weak; I wouldn't claim these things have been found to be false, exactly, but they don't seem well supported.)