We both know my comment was about a spell
If someone suggested that it was outrageous for a wizard to shoot a bow, and there was a response of "cast Magic Missile", I don't think that would create much controversy.
Similarly, using DEX/Stealth is how a non-caster achieves the functionality of an Invisibility spell. My initial reply to you was mostly intended as humour; what's surprised me is that has generated all this contoversy.
Or by normal vision by simply walking around the box you are hiding behind. "Keep Out of Sight: If you no longer have any cover or concealment against an enemy, you don’t remain hidden from that enemy."
Or by normal vision with with a simple perception check on the part of the person you hid from. "An enemy can try to find you on its turn. If an enemy makes an active Perception check and beats your Stealth check result (don’t make a new check), you don’t remain hidden from that enemy."
All you're pointing out is that, if you cease to be hidden, then you cease to be invisible (which is a consequence of being hidden). I don't see what interesting thing you think follows from this fairly trivial logical point.
If the target of an Invisibility spell makes an attack, then s/he ceases to be invisible too. All these conditions have various ways they can be defeated or come to an end.
There is no need for Blindsight or Tremorsense since the person is unseen, not invisible.
There is no need to use Blindsight or Tremorsense to spot a person under the Invisibility spell, either. Dust, a bag of flour, a cloak dropped onto them (perhaps - adjudications might differ on this one), etc, will all allow that person to be seen.
Or, perhaps the 4e PHB2 just explained the concept in a hurried or non-optimal fashion. If you have to pass a stealth check, in order to not be seen. it seems almost obvious that you are blatantly visible, with stealth causing the passive perception of invisibility.
The PHB2 isn't hurried or non-optimal. It's making the point that someone who is hidden (in virtue of a successful Stealth check) is in the same state vis-a-vis those from whom s/he is hidden as is a person under an Invisiblity spell, or the target of a successful Eyebite attack. In all these cases, while the condition obtains the invisible person can't be seen by the relevant targets.
Of course the fiction is different in each case. This is reflected both in the circumstances necessary to generate the invisibility, the various targets to whom the character is invisible (hiding - the ones from whom s/he is hidden; Eyebite - the one whom s/eh hit with the attack; Invisibility spell - anyone not able to detect him/her with Blindsight, Tremorsense or one of the techniques I suggested earlier) and the circumstances that bring it to an end.
But that different fiction is secondary when we're thinking about core functionality.
