So ...
Either box of Junk, or box of Treasures ...
Or box of Junk, or denial ...
Or denial, or box of Treasures ...
Yes?
No denial, or denial situation.
......
No, still not getting my point across.
There's still only two possible outcomes, success or failure. You just might not be able to tell for sure if you succeeded or not because the results were ambiguous.
But yeah, i gues i would question my DM if there would be no way for me to say if i pased or failed.
If i may use your example ... if i would try to [PERSUATE] those people to accept my help, and lets say i would roll 20 (or in general big, lets say 15+, number) and they would tell me "no thank you help is on their way, we are good" ... i would question what was the point of that roll, since im quite sure i passed and yet they dont really seem persuated to let me help them.

Because that polite denial could have been the success when the failure was them being a lot tougher than you and kicking your ass just for asking.
Wich i presume i would find out in either different playtrough, or after reloading ... by them just telling me?
(I mean, if they really like me, it wouldnt make sense to keep that information secret, right?)
It would make sense if they were, for instance, organized thieves and happened to like you but weren't about to tell you their ambush secrets...
Just my thoughts and ideas in any case.