I'm just going to go with the mask stuff because it makes the most sense and with a story with amazing plastic surgerythst makes someone look identical to another and hypnosis, I don't think it's far fetched.
I hate to defend the stupidness of it all since Big Boss even has both eyes working, bit at least the mask tech actually works out. If we don't assume the Raikov mask was at least something as good as this theoretical Ishmael mask, then how did he get anywhere with it? Why would Volgin need his specially developed groping identification technique?
BTW, I hate to say it, but the mask
even was capable of blinking (around the :57 second mark). Still doesn't excuse the working eye though. Maybe that's another revelation this game gives us, Big Boss got the most advanced prosthesis compared to Venom, a cybernetic eye! And he just kept it hidden in order to surprise his enemies if need be. If he showed it off to Solid in MG2 though, Solid probably just went "eh, whatever, 'what a twist'" and torched BB shortly thereafter.
I prefer the "hypnosis theory" though. Don't know if it is a widely held belief or anything, but Ishmael's visage probably looks more like BB to the other observers in the hospital scene, still bandaged and disguised, but screwed up eye, beard, the works. It's clear looking back that Venom suffered from hallucinations when looking at the mirror the doctor held up. He sees BB's as his "original face", briefly sees the "new face", and then sees BB's again. In that version, Venom then appears to not have his face changed, except he still sees his original face in the mirror, implying the plastic surgery has taken place.
I'm not at all suggesting that only Venom saw himself as Big Boss and everyone else saw the player's custom avatar, that just doesn't work at all for a number of reasons. What I am saying though is his perspective is obviously unreliable, also shown by his hallucinations looking at the mirror at the end of the game. I believe the best explanation is that BB was "hypnotically disguised" to Venom. He couldn't see underneath the bandages so to speak, even if technically he should have seen a beard, he didn't because he was conditioned to be unable to identify a "double", at least until his programming was broken by one of his handlers (AKA Big Boss at the end).
Also (completely random MetaGearSolid.org comic):
Subscript on the Meta Gear website says:
"Don't knock it til you've tried it, Kaz. Here, take some."
Comic is a mostly defunct one that the site creator put up once in a while, still pretty funny most of the time, even though there aren't that many comics (27!). It's name is "La-Li-Lu-Le-Lol". The real treasure is the main content of the website which consists of Metal Gear critique and analysis.
If you've heard of the MGS2 VR theory, this guy did it. One of the better sources of Metal Gear analysis, the bulk of the material is from a while ago though, like around the time The Snake Soup was a bit more active with new articles.
Classic site (up to around 2010 with PW I think):
!!!
Modern site (more blog like, some new stuff including a TPP review which makes some good points IMO):
!!!