Check out this passage.
It defines hidden, for game purposes, as "unseen and unheard". Unseen is synonymous with heavily obscured. You can't be one and not the other, not with reference to a single observer.
I think that part of the problem is that obscured is a subjective term. You can be obscured from the point of view of one creature, while another creature can see you clearly. If my back is to you, you are heavily obscured to me, no matter what the lighting or other conditions are like in the room we're both in. The area on the other side of a dense hedge is heavily obscured to an observer on one side, while to an observer on the other side, it is brightly lit, and the area in which the first observer stands is heavily obscured.
The term obscured only has meaning with reference to a particular creature's point of view.
To be hidden from a creature is, by definition, to be heavily obscured from that creature's point of view. The exceptions to this general rule are Mask of the Wild, Naturally Stealthy, and Skulker. If you are trying to hide, you need to have some means of not being seen. The phrase, "You can’t hide from a creature that can see you clearly," doesn't mean that you can always try to hide from a creature that doesn't see you clearly. It hasn't waived the "requirement" that is still to be found in the rules, that to be hidden, you must make yourself unseen and unheard, since that's the meaning of hidden.