Perhaps the Puma could not (it might...) - but towing in heavy sand is where massive torque and power is a very helpful thing. When its vehicles by themselves the difference in weights is a big thing. Its all relative. I am not having a go (god forbid) at the D4 what I am saying is that with just the vehicle the weight of the D4 works against it in soft sand versus the Puma (and that is just a fact). There are also tyres which is very important but again I wont go into that cause its touchy. Now put the same power/torque in the puma and watch it become better in sand than a D4 towing (because it is a ligther package and has great big tyres). In terms of weight being a big thing, think the old Zuk's and even further back the Model T Ford - despite skinny (yet tall..read shallow approach angle for the tyre...) it was exceptionally light and allowed the car to go through deep sand with a puny engine - now attach a 1.5 tonn camper and its not doing anywhere.
My D2 recently had a dose of 4.6 litres and in the softest powdery sand from 700rpm it just pulls out like a steam train from walking pace. Its crazy. Then again its got 31 inch tyres on 16's too and they are aired down to give a nice long footprint. So the ideal sand vehicle is gobs of torque and power combined with good tyres and low weight. The D4 is good in sand despite the weight and tyres, which proves what a great powerplant and gearing it has. Lets not write off peoples experience however with other models of the brand - ie the above post about the poster's son's Puma. He is also not the only one who has made such comments over the years. Now sure put a big load on the back of each vehicle and point them up a steep sand hill and the D4 3.0 TT should do better.
Cheers
