Phil is right.
Altitude is much less important in a reentry than velocity. The "recreation" suits drop from essentially zero velocity platforms, and the atmosphere, even at 60 miles, begins to slow you down soon after the drop.
Drop somebody from a fixed platform about a thousand miles out in space and you'd have another situation altogether.
A return from orbit, as you point out, is another issue. In fact, I suspect that the velocity of the Columbia at its breakup point would have exceeded the capacity of one of these suits without additional shielding such as that shown in the MOOSE design.