This sounds like completely made up rubbish to me. Reflective surfaces definitely absorb less heat. Mirrors may however be impractical and may not reflect enough to make the missile immune.

Or have a lower melting point, making it more practical to use some sort of heat-resistant armoring? Might be pretty difficult to make something that both reflects light and is heat-resistant, no mirror reflects everything.

I think the usual issue is a mirrored surface is not robust enough to absorb extreme levels of energy for very long before it becomes a poor mirror.

I expect the counter will be more along the lines of having sufficient ablating material to block the laser - a small amount of extra armour probably has an outsize affect on survivability.

Just spitballing here but it might have to do with the fact that materials that absorb light are more heat conductive than materials that are reflective.

The SR71 was famously painted black as a mitigation for surface heating issues because the black paint conducted heat away from the areas the were really susceptible to ram-heating.

Perhaps reflective surfaces reflect some percentage of the incoming energy away, but thermally conductive surfaces conduct a larger percentage of that energy away and are able to safely sink it into some thermal mass.

Black surfaces are good at absorbing AND radiating heat. I think that’s why the SR-71 was painted black. The amount of heat it got from absorbing the sun’s rays probably paled in comparison to the heat it radiated from all the friction as it flew.

From what I understand, the SR-71's black paint did radiate thermal energy, but also made the plane harder to see in visible light at night, and on radar. It was a RAM coating impregnated with iron to reduce the radar cross section. The characteristic chines along the edge of the fuselage were also meant to reduce the radar cross section.