People just think they understand ethics, even if they don't.
"Don't break the law" is an incredibly poor foundation. Many laws are ill-conceived, ambiguous, overly broad and widely ignored or manifestly unjust. Using this as the basis for ethical behavior would require you to be unreasonably conservative and pedantic while regarding complicity in an injustice as ethical behavior. (It also implies that you could never use ethics to inform what the law should be, since it would just tautologically be whatever you make it.)
"Don't knowingly cause net harm" is at least as valid, but then admits the possibility of curiosity-based shenanigans that could lead to the revelation of a vulnerability that saves innocent people from the consequences of it being later exploited by someone nefarious.
> Putting in that password on a system you don't own without any sort of permission to do so is very clearly against the law.
Driving 1 MPH over the speed limit is very clearly against the law, even if the orphanage is relying on you to have the funding letter postmarked by end of day.
Walking your date home while you're intoxicated is very clearly against the law (public intoxication), even if the alternative is that they drive themselves home while intoxicated.
Ethics is something else.
> The only ethical path is to let them know you have some reason to believe they are not using secure passwords or whatever.
But you don't, really. Your belief may even be purely statistical -- suppose you expect that if you try the default on many servers at different companies, there will be at least one where it works, and you'd like to report it to them, but you have no idea which ones unless you try.
> It just isn't the white hats problem.
If you have the capacity to prevent likely harm and instead do nothing, what color is your hat?