No, my interpretation is that the Invisible condition is not necessarily One Ring-style invisibility.
The invisible condition is the entirety of the effect granted the invisibility spell, so unless the condition is one ring style invisibility, the spell doesn’t grant one ring style invisibility.
It is a condition being used to describe a creature being unseen, whether by hiding out of sight or using magic. The Invisibility spell turns you invisible, One Ring-style, but the game effect of that amounts to the same thing as being in pitch darkness or successfully concealing yourself behind intervening terrain, except you don't lose it by making any noise louder than a whisper.
If the game effect is the same, then either the game effect of being in pitch darkness or successfully hiding yourself behind intervening terrain must include remaining unseen when someone illuminates the darkness with a torch or moves so that the terrain no longer intervenes from their perspective, or the game effect of having the invisibility spell cast on you must not include being unseen while illuminated and not behind intervening terrain. Either interpretation is unacceptable to me.
Note that this is how it works in the 2014 rules too, just explained differently.
No, it isn’t. The 2014 rules account for being unseen and undetected separately (though admittedly it’s phrased awkwardly); hiding grants the latter under the condition of the former but does not grant the former on its own, so you need suitable cover or concealment to prevent you from being seen, and invisiblity grants you the former at all times while the spell lasts but does not inherently grant the latter, though it makes the latter much easier to gain by hiding, since you no longer need cover or concealment.
Everyone is fixating on "hiding makes you turn invisible somehow" which, yes, sounds ridiculous, but the Invisible condition has a specific meaning that, if you look at the actual game effect, doesn't particularly strain credulity.
Again, that’s a reasonable interpretation, except that it would mean the invisibility spell, which only grants the invisible condition, must also only grant this mechanical effect and not actual invisibility.
At worst, you're looking at a situation where a PC gets advantage on an attack roll on the same turn they break cover. Like, so what? Let the Rogue sneak up and slit a guard's throat. That's what Rogues do.
That’s not the worst. The worst is a situation where the PC goes somewhere there are no enemies around and repeatedly rolls stealth checks until they get a 15 plus, and then walks straight through a maximum security area (describing themselves being super, super quiet about it, of course!) completely undetected. Or, if you favor the “the invisible condition isn’t actual invisibility” interpretation, the worst is a situation where the player casts the invisibility spell and tries to sneak through a maximum security area, only to be told, “sorry, the spell doesn’t actually make you invisible, it just gives you advantage on attacks and initiative rolls.”