The horizontal control is second order, which locates the marker within a centimeter, but the vertical control is not so well established.
The DATASHEET says, "The orthometric height was scaled from a topographic map."
And it does appear to be on a rock (the highest point on the summit), if not a pile of rocks:
"THE MARK IS A UNITED STATES GEOLOGICAL SURVEY ALUMINUM DISK,
STAMPED 14502, CEMENTED IN A DRILL HOLE IN A 5 BY 10 FOOT
BOULDER PROJECTING 3-1/2 FEET."
A leveling survey tied to a quality benchmark is the best way to settle this. I recall seeing a thread by Doug on the MWPS forum contemplating that effort.
GPS might also be adequate, if proper techniques and correction are done. Here's an old article (1990 )but written in lay terms:
Establishing Vertical Control with GPS
