Yes, it is just as important for open baffle speakers as box speakers to have a stiff baffle. Spatial uses a thick wood material (I think it is a composite of some kind). PAP uses metal bracing to reinforce their baffle panels.
My open baffle speakers (based on GR-Research designs) use a separate enclosure for the woofers to handle the bottom three octaves, built with 1.5" high quality MDF. The second enclosure handles everything else and is built using a composite material.