In Metal Gear Solid, why did Foxhound need Snake?

Metal Gear Solid is a tactical stealth-ops game wrapped in an enigmatic nuclear-themed storyline. One part of that storyline has always bugged me.
Halfway through the game, it comes to light that, in order to launch the nuclear missiles on Rex, the terrorists need either two detonation codes, or three card keys. They lose the ability to use the codes, and so are dependent on finding the card keys.
And for some reason, they need to let a stealth operative into the military complex they took over so that he can find it for them.
This doesn't exactly make sense to me - why would Foxhound need to bring in someone who knows less about the military complex than they do? Why would they need him to find the keycard, when they could just search the base themselves?
Yes, it's being held by Meryl when they found her, but they had her in captivity until Snake arrived. Had they just done a better job of searching their prisoners, they would've found the keycard no problem. She can't even resist their psychic's mind control, so he could've just found out if she knew where it was, and taken it from her.
Where, in all of this, is it necessary for them to bring in Snake to find the keycard for them?
Note that while a full explanation of how things went down is fine, all I'm really looking for is Foxhound's original plan, and how it required Snake.
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Was Solid Snake in FOXHOUND?
When David joined FOXHOUND, he was assigned the codename Solid Snake by then-commander Big Boss.When did Liquid Snake join FOXHOUND?
He was eventually reunited with his old ally Mantis and the two joined FOXHOUND in 2000, with Liquid becoming its squad leader after Snake had already retired from the unit.What does Snake mean in Metal Gear Solid?
Kojima wrote on Twitter to explain the code name Snake in the original Metal Gear. "The reason I used Snake as code name in MG was Snake was the most appropriate symbol of living thing that hides his presence and sneaks without any noise."Why did Drebin inject Snake with FOXDIE?
Drebin also provided Snake with an injection of nanomachines so that he could operate any weapons he might purchase from him, though he secretly infected him with a new strain of FOXDIE, which was programmed to kill former Patriot members Big Mama, Liquid Ocelot, and Big Boss.LORE - Metal Gear Solid Lore in a Minute!
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