Okay, I would like to copy the pages but this is obviously not possible withouth permission of the authors, so in short:
I know about the socalled 'Janda-situp' (the term is definitely not from Vladimir Janda himself) and used it on a more or regular basis since 1987. Back then I bought a copy of the book Manuelle Medizin from Karel Lewit, Sachse and Janda were among many others gems this exercise is described and analysed in detail.
The reason they recommend a situp without support is that you cannot cheat this way (at least if you don't use momentum), so you either do it right or cannot do it at all, and that it teaches the correct coordination/timing of abs, glutes, ischiocrual muscles and psoas etc during the situp. The reason they give to use a support at the back of the leg (actually the picture shows either a person giving the support or a simple sandbag in place) is NOT that this would inhibit the psoas but to fascilitate the gluetes so that the pelvis gets in the correct position for the situp.
The support on the backside of the legs is meant as a help for beginners, but
ultimately you have to be able to do it without any support...
Should there be errors in my description/summary these are of course mine not Janda's.