Agreed. Passive is a HORRIBLE term for this. "Repeated or Secret" is better since the DM can also use it for "secret" rolls.
Yeah, it really doesn't make sense but if you want to play it that way, knock yourself out.
FWIW, "helping" and working together should not be allowed if the people "helping" have disadvantage. I know that isn't the "rule", but I also know most of the rules in 5E are imbalanced, over-simplified, or ill-conceived.
EDIT: I'll go further to say that this one phrase for working together ruins it:
A character can only provide help if the task is one that he or she could attempt alone.
It is a stupid condition, because frankly speaking,
anyone can ATTEMPT anything. It makes it a non-issue and superfluous. The condition should be:
A character can only provide help if the task is one that he or she could accomplish alone.
It is a big difference.