I think that in BLD if caught cheating it should be a DNF but in the case of being caught cheating from during inspection i could understand a DNS because he didn't actually start the solve correctly. But in bld say I just took my blindfold off in the middle of a solve and did some moves then put it back on now if my judge noticed that would be a DNF but if my judge didn't notice and found out after the fact that would be cheating and you want a DNS for that which is confusing to me at least.
The problem is that when someone has all DNFs it looks like they just fail hard at cubing, when instead they have been disqualified. The way I see it DNF is for when they go up and do a solve and fail at it, whereas DNS is when they either never did the solve or the solve was retroactively annulled (i.e. it never existed). For your example it should be DNF because they realized (after the fact) that the solver failed hard at actually solving - the solve itself wouldn't be annulled, they just changed the result later on. (Doing moves after you take off the BLD results in a DNF of the solve, not a total disqualification.) Changing a solve to a DNS would only be done when you find out someone cheated and you want to remove their solves from the database.