I'm inclined toward the latter. I've never heard of compression braking harmful to a transmission. Certainly, it is completely normal for trucks, and in fact trucks are frequently equipped with devices which increase the effectiveness of compression braking. I'm not seeing a reason why compression braking would be any more harmful to a gear train than accelerating.

My father worked on a project at 3AD RAAF Amberley in WW2 on a project to spin the mains on B-24 Liberators to save tyre wear. Ultimately the project faded away and the war ended.

Heel and toe technique - initially developed to ensure that when the rear tyres were lightly loaded braking down to a corner that the sudden imposition of further braking forces when you lift off the clutch in a lower gear didn't give you compression lockup.

A very usefull technique as it makes driving smoother and at the cost of a tiny fraction of fuel reduces wear on your clutch and engine mounts.

One useful bit of information regarding gears is that if the efficiency is less than 50% then they are not reversible. i.e the output will never drive the input. This is most often seen with high ratio worm gears, such as used in car jacks... when you stop turning, the weight of the car does not spin the handle in the reverse direction...
Gears- Gear Efficiency
For normal car gearboxes, the efficiencies are over 95% so can be turned both by the engine and by the wheels.
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Now where were we.?... Ooh yes pre-spun aircraft wheels....