[nkmnz]

You are right in the literal sense of "burning fat" = oxidation of triglycerides. I'm used to a more figuratively use of the term in weight loss discussions, referring to "losing body fat", which is the result of total calorie deficits, increased fat oxidation and reduced fat synthesis. Depleting the glycogen storage helps to reduce fat synthesis from ingested carbohydrates, so even if the fat molecules aren't burned directly due to the higher intensity, you'll lose more fat tissue with higher intensity.

But again, yes, in the literal physiological sense, you're right.