Do you have double top wires on fences, above the stocknet, routinely in that area? If so then it is the fencing causing these injuries. On one estate I used to stalk adjacent to the A6 and largely on "moss" land near the Cumbrian / Lancastrian county ditch there was a lot of fencing erected by one contractor which had two plain wires on top above the stocknet. It was lethal routinely catching fallow who dropped a rear leg between the wires and twisted them tight as the deer's (usually rear) leg windlassed the 2 wires for the first half turn. Rarely could one extract a deer alive - a few fawns over a lot of years. It took a recognisable proportion of the cull annually - 2 or 3% of their mortality on its own and produced a number of lower rear leg limbed deer. Having once lost a part of a limb though I found that 3 legged deer were almost invariably fatter than their fellows by sex and age at the same time of year; presumably from moving around less. This applied to the other species (red and roe) in that area also.
So to answer your original question - the answer is "B******ks do I believe it" any more than I suspect you do. Poachers are like the poor; they are always with us, but this is as you suspected the fencing which is to blame.