It doesn't lead directly. Payton said on a 1up Yours a long time ago that they have a very big bible with numerous stories to tell. They could easily pick it up after and show Big Boss' further developing desire to have a place where soldiers are respected. This is really only implied in the very end of Portable Ops.Kastro said:Portable Ops leads pretty much directly into MG1 with Big Boss establishing Foxhound at the end of the game, etc.
Why would Gray Fox have Raiden's suit that wasn't developed until after Gray Fox already died? He also wasn't even a cyborg prior to Metal Gear Solid
Gray Fox theory makes less sense than Sunny.