Though I have no idea of the circumstances of this sad event, Sometimes pilots climb away at a more slow airspeed after takeoff, sometimes that speed can be slower than a relaxed glide speed. That means that in the case of an engine failure, it could actually be necessary to dive to accelerate to glide speed. Couple that with the fact that the Tiger Moth is not streamlined - it does not carry its energy well after reducing power.
My last flying in a Tiger Moth was the maintenance check flying following a ten year restoration project, the possible need to glide was always on my mind during those flights, and I stored energy the best I could in the 'Moth...