No? Scientific experiments should work to rule out alternative causes, that's the whole point of it. Introducing a lot of structure to someone's life that was previously very unstructured (as diet often is in mentally unwell people) could be part of the reason their symptoms improve, rather than necessarily the diet itself. It's an alternative cause that I think should be ruled out before assuming it's the content of the diet itself that caused the difference.

Control groups are not "whataboutism". If adding that kind of control showed keto was specifically helping these people, then that'd be great; but since the study doesn't seem to have done that, it's hard to be confident in the conclusion.

Instead, they gave the participants cookbooks, and assigned them a personal coach to help them plan and cook their meals and follow through with the diet change. Giving that kind of personal support to change habits and make more considered choices to someone with mental health challenges is bound to make them feel better, no?