If you analyze the Sioux City crash, the aircraft seemed to be sliding right side up until it went into the corn at which time it started to cartwheel, somersault and break up.
I'm not a pilot, so I can't answer the question in a relevant manner, but I don't think it was the simply the transfer from runway to grass that caused the aircraft to dig in and flip, so much as they'd lost the right wing and right MLG very early in the crash sequence which pulled the aircraft violently to the left and introduced a rotational moment about the yaw axis. I personally believe that even if the whole area was paved the aircraft still would have flipped over simply because of the amount of kinetic energy they had at touchdown, as both their approach speed and sink rate were way in excess of what the aircraft was designed to take.
Obviously leaving the paved area did have an effect, but if you're going onto concrete with an excessive sink rate then it's not likely to matter what your horizontal deceleration rate is.