Hot Rod article on 70 Barracuda trunk floor

Yes, it can be tricky to structurally secure the body. I designed thrust stands for rocket engine tests. To support a rigid body in space requires 6 independent supports to resist 3 force directions and 3 moments. Ex. to secure the top seat of a 3-legged stool with (thin) legs bolted down (resists vertical motion and 2 tilting moments off horizontal) also needs 1 side support (resists 1 horizontal motion), and 2 side supports in other direction (resists 1 horizontal motion and a twist about the vertical). When a designer misses a support, whether building a thrust stand or bridge, things can move that shouldn't. People often miss supports needed to resist a twisting moment.

That said, an early This Old House episode had them spend a lot of time supporting a roof before knocking out a load-bearing outer wall. After they did, they found the roof held up fine without the temporary supports, which is typical in a house with all the roof framing. People here have posted photos of convertibles which sat with the frame on the ground so the frame was totally rusted away, yet the body still somehow held its shape and the doors closed without binding. Perhaps the thick steel beams in the kick panels (convertibles only) were still solid.