Noctem
Explorer
The "usually" is there as a qualifier, in case you are actually invisible or hidden by falling snow or whatever. It basically means "unless there's something stopping it". And popping up from behind the rock is approaching the creature, even if you're still twenty feet away - you're closer than you were when you were behind the rock.
I mean, you could make a case to the contrary, but you'd really have to press it and hope that your DM was inclined to also choose that interpretation. It really seems like a stretch. Both the letter and the intent of the rule seems pretty clear in this case.
You have no grounds to restrict what the text means by usually to only be related to invisibility or other specific scenarios you designate. You simply don't have that authority. It's there to show that the rules for leaving hiding and approaching a target are not absolutes. You are treating them like absolutes. You are incorrect in doing so.
Approaching someone and simply popping your head out to see your target and attacking is not the same thing. That's a ridiculous claim and I'm sure you know it. The rule clearly states "leaving your hiding spot" which implies movement from one point to another outside of that place. In a grid setting that's at least 5 feet of movement. Then once you've done that, if you used movement to move toward a creature or at any time, the creature will usually see you. There's 2 requirements here. Physically leaving your hiding spot and approaching a creature. You need to stop speaking in absolutes and actually read what you're quoting.