I agree the results are surprising but we are missing an essential piece of information: Did the reading return to 65kΩ when tested with the DMM *after* the 500V IR test, i.e. were the two tested values repeatable under their respective test conditions?
There are a couple of possibilities. A continuity test typically applies a few volts maximum, during which the power dissipated as heat into 65kΩ is negligible, say 1/65k = 15 microwatts. The power dissipated when subjected to 500V is 25,000 times greater, at 3.8W. In fact most IR testers won't output this much power; the voltage drops off when the resistance is this low, but there is enough to drive off a thin film of moisture at the exposed ends of cables and terminations. This can cause a moderate IR reading to rise under test and not immediately fall again afterwards.
Another mechanism something akin to what Marconi describes is called dielectric absorption, which also tends to cause varying resistance readings. When insulation is subjected to high DC voltage, some molecules in the material tend to align so that their electrostatic dipole lies parallel to the electric field created by the voltage. When the voltage is removed, these molecules don't all instantly return to their original positions, but as they jiggle back into random orientations, their stored energy creates a voltage across the insulation that can sometimes be read with a DMM, and which can cause incorrect readings on a resistance test. The effect isn't usually noticeable in low voltage electrical work, but in both high-voltage transmission and precision analogue electronics dielectric absorption is a daily fact of life that has to be worked around or compensated for.
Finally, a British Standard Woodlouse standing across two terminals measures 65.3kΩ. They can run quite fast when chased by 500V.
HHD: Can you add any info, such as relative polarity of the tests, type and age of fittings and cable etc. 65kΩ is low and its cause ought to be identifiable, regardless of the anomaly you describe. Have you checked the calibration of the MFT continuity ranges at all in case that is a gross measurement error?