"...they need to do it on foot." or horse (guide, catered meals and luxury wall tent included), snowshoe, ski, dog sled, snowboard, canoe, inflatable raft, kayak, or fly in if it is the Frank Church.  There are plenty of mechanical uses in the Wilderness.  In the first minutes of the Wilderness Society, Bob Marshall listed the mechancical invasions that along with cars, airplanes, and motor boats they were worried about, "..Railroads, Cog Roads, Funiculars, Cableways, etc."

Go back to the Wilderness Act , and replace "no other form of mechanical transport "  with either mountain  bikes or ..Railroads, Cog Roads, Funiculars, Cableways, etc.. Which makes more sense.

 "...there shall be no temporary road, no use of motor vehicles, motorized equipment or motorboats, no landing of aircraft, no other form of mechanical transport, and no structure or installation within any such area."