This is ridiculous.
... the exact opposite side of the Earth from the Great Pyramid?
An easy claim to check.
Various sources say the pyramid lies at: 29°58′45.03″N 31°08′03.69″E
Thus, the "exact opposite" is at 29°58′45.03″S 148°51′56.31″W
So for a start, your guy is lying to you.
His "interesting" object at 32°30′07.74″S 149°52′46.51″W is actually 296.6 km (184.3 miles) away.
What a liar.
Actually that is fairly close to being antipodal, all things considered. Then there is the fact of plate tectonics, too, so perhaps it used to be even closer to the antipode -- although 4000 years x's 10 cm/yr (an upper bound on plate motions) is only 0.4 km.
Then there is the fact that there were actually four great pyramids, but the Romans dismantled one for construction materials. This would cause there to be four lines dividing the earth in four parts, but they should all again coincide at the antipode.
My guess is either glitches or seamounts, although usually seamounts lie in chains.edit on 28-10-2013 by MrInquisitive because: (no reason given)edit on 28-10-2013 by MrInquisitive because: (no reason given)