My understanding of how engines work tells me that's nonsense; a well driven and appropriately geared
diesel will easily outstrip an equivalent N/A because you can reasonably run the engine at lower speeds and reduce frictional losses for a given output - in fact, that's true of petrols as well... I could never get much more than 35MPG out of my old Lag 2.2D, where my neighbour who had a similar aged, similar mileage 2.2TD would consistently get ~5-10MPG more than me with similar round-town journeys.
I can't think of very many 'modern' N/A automotive diesels - for precisely this reason, but if you look at some of the last made, like VW's 1.9 SDis, the TDis are appreciably better on fuel and have lower CO2 emissions despite being more powerful and architecturally identical otherwise (I think they even did a PD SDi?.) I'd imagine if you drove them as 'slowly' as the SDi, you'd get not just a bit, but much better mileage. The problem is people using the extra power (e.g. combining the extra air with extra fuel), not it being there.
If turbos make an engine less efficient, why is it that recently, even commercial, ship-bourne and other static engines which have traditionally been hulking great N/As are being replaced with turbodiesels, accepting the compromise of potentially reduced reliability when there's not much concern for the weight of the drivetrain?
And these are two engines of the same capacity, despite the extra kerb weight of the TDi. If you used a smaller capacity turbodiesel with the same output power as the larger N/A, you'd wipe the floor (especially since you'd probably still end up with more torque, available lower down.)