Thank you KE7GKP. Yes, I was surprised to (I thought that it only happens on cheap wall wart chargers), and it's cheap chinese indeed, rated to give 5.5 output and giving 5.6-5.8 - I need to take it apart to see what regulates the power. But as I am really experimenting at the moment, I think I can live with a cheap chinese for a while, even if it breaks after a month
I know that a final project will require something better to provide fault-free, stable operation (but first I need to know how the final project will look like and what power requirements will be).
I'm also not quite sure about my meter, as it begun to show weird things recently (I think it's cheap chinese inside too as it is not a "can't-afford-Fluke", but I sort of inherited it, so I can't complain).
Anyway, thank you for all info - my Arduino uses a real crystal, so I feel reasurred by your post. Thanks!