I don't see any reason to doubt it. An extremely clean airframe with A LOT of thrust should be able to hit that speed.

Regarding the use of a GPS. He might be off by a few percent plus the wind component but it would be very close. Boeing has faith in GPS. We have two in the 747-400 I fly and crossing the Atlantic along the organized tracks we split the centreline of other GPS equipped aircraft as we pass them at M .86 !