The original claim is not wrong. Thinking hard does not burn significantly more calories.

If it’s really hard to measure because the amount is so small that it requires precise equipment, it’s not significant relative to the rest of the body’s energy expenditure.

The increase due to thinking hard is small, but still, the amount of energy burned by your brain is very significant. It consumes around 20% of the total calories your body burns. It just doesn't spike due to intense concentration or mental activity.