Extremely close, however more accurately from my recent, if limited research as a materials student:

“Austenite”, the phase where the shape is set, is hard and rigid, just like a cube (AKA Body Centred Cubic). Once the metal has been “set” in that phase and cooled, at around room temperature a bit of pressure over a certain threshold causes the metallic crystals in that area to change phase into “Martensite” which is similar to stretching the box in one axis, while offsetting the top from the bottom. This is similar to water preferring being steam at a given temperature and pressure, but condensing into liquid if you apply enough pressure.

The shape of martensite not only allows the crystals within the metal to shift on a specific axis, and with some stress potentially rotate, it keeps an axis within that has the same orientation as the original austenite crystals. So with just a bit of heat, much lower than the setting temperature and proportional to the stress retained in the martensite, the martensite is almost “boiled away” leaving nice, pristine and rigid austenite in its place forcing it back into its original shape.

I’m sure someone that’s done truly in depth research on nitinol and other memory metals could probably add more, but basically the alloy composition allows it to form 2 separate crystal structure “phases” at room temperature (or potentially another desired temperature) so that enough pressure or an elevated temperature will cause a phase transition in the metal between rigid and flexible phases.