Well, I guess I'll weigh in here.
In the case of supersonic capable aircraft, the reason for the use of a stabilator is for controllability due to the normal shock that is created at the corner where the elevator and stabilizer are joined in a conventional configuration. This shock creates relatively very high pressure aft of it, which is very hard to overcome. Additionally, the only part of the surface that is creating ANY force is the deflected part, so you have a very heavy control that is very ineffective. Aside from creating problems in adjusting for the changing position of the center of pressure (mach tuck, for example), it obviousy does not give the maneuverability that a tactical aircraft requires.
I have not really looked too much at light aircraft design issues, but can offer some speculation. Without looking into it in more detail, it is possible the issue is actually the same some low speed aircraft. For what ever reason, the design might be, essentially, too stable. The amount of control effectiveness is just not enough, so they go to the stabilator. Again, this is all without looking at the specifics of the design, but just offering some directions for consideration. Perhaps the aircraft needs to have a more forward CG due to some other handling problem that was encountered during flight test.
Just as probable a reason could be that it needed more authority in certain flight regimes, i.e., they found some corner points that needed more control. In fact, as I think about this, that would make a lot of sense, in that the anti-servo tab would be less effective at lower speeds, so you would have a lot more authority there (in terms of stick force/G) to offset any handling problems, but, as speed increased, the tab would dampen out some of the over-control problems inherent in the stabilator design.
In any event, it is not unlikely that these aircraft were initially designed more conventionally and the stabilitor was added after some flight test issue.
Now, on the Bernoulli vs. Newton thing, this has been discussed often here and elsewhere. It is not a "combination" and it is not "one vs. the other". Bernoulli's equations are based on Newtons. It's as simple as that. However, those that use this "weight of the air moving down" thing, while that may be true, it is after the fact. That is a RESULT of lift, not the CAUSE of lift. This comes across to me as a basic misunderstanding of Newton's laws in the first place, like those that think that an untied toy balloon will shoot across the room due to the air moving out, so it is having an equal and opposite reaction. No, that is not how it works. The balloon moves because it is PUSHED, just like the wing does, and no, it is NOT the air rushing out that is doing the pushing!