In Metal Gear Solid 3D, does the player lose the 3D effect as a narrative mechanic?

Rumours or anecdotes online have suggested the following but without a copy of the game to test I wanted to inquire as to its veracity:

In Metal Gear Solid 3 the player can switch between third and first person gameplay. In the 3DS port of the game one would reasonably expect the first person mode to use the 3D capabilities of the console - however said rumours implied that following the loss of Naked Snake's eye, the 3D effect is disabled to reflect his (and therefore the player's) loss of depth perception.

I haven't found a source with a definitive answer - is this true & accurate? It certainly seems in character for a game that has several other notable examples of Devs Think Of Everything, yet at the same time this mechanic means disabling the defining feature of the console, in effect making the entire port redundant!

Does the player's first person view on 3DS really reflect Naked Snake's loss of depth perception?