Thank you to the local tuning specialist for providing the data.
This time for review: G31, 540i with B58-series engine.
The tuning specialist claimed that the torque was increased from 450Nm to 550Nm. For a full 100Nm! Impressive gain! Is it really so? 

Here, with black – the new curve, with red – the initial curve. 
I marked two lines with green: one for 450Nm reference, another for 550Nm reference.
What conclusions can we draw?
a. initial curve – either BMW has given more than offered, or the stand slightly “decorates” the result;
b. tuned curve reached the proud 550Nm (we see the automatically generated mark) at around 2100 RPM in a very narrow stage (we could say – spot), in no other place it reaches more than 540Nm. The average torque is 530Nm above 4500 RPM (this is the range that is actually used in the case of an automatic gearbox).
For example, in the range around 3000 .. 3500 RPM, the torque difference (increase) between both curves is closer to 50Nm than 70Nm, not even talking of 100Nm. The declared difference of 100Nm, possibly, is reached in the range of 5400 .. 6000 RPM. 
Of course, 100Nm sounds much more impressive than, for example, 65Nm. 
Yes, it’s true – if the automatic gearbox is used, the increase of the torque in the range of 5500 .. 6000 RPM is incomparably more significant than if in, for example, the range of 2500 .. 3500 RPM (the gearbox does not use this low RPM range in the kickdown mode). But, if the manual transmission is used, the situation is opposite – exactly the range of lower RPM is used much more often.
I will not repeat the topic regarding methodology of the measurements (you can read in other blog entries), will not talk of simple tricks (how we initially take the worst result, as tuned – best of attempts, etc.). This stays on the conscience of the tuners. This was an example (without disputing that the curves show an increase in torque), of how it is possible to manipulate the data even as if without lying. 
If we talk about absolute numbers, the graph shows that this time, 550Nm, there’s no way around it. The result is closer to 530Nm. And if from the initial curve “squeeze” maximum with the same energy as from a tuned one, my gut feeling says that the increase from 500Nm (which is offered by the Performance and Sound kit) would not be so impressive.