Do you know for sure this is the design?
How can I be completely sure if I haven't disassembled one of their pickups?
But what else could be in there as flat as the pickup is?
The Underwood/Shadow SH-950/951 has a piezo crystal about 2 mm thick sandwiched between a bent piece of brass. That's definitely not what could be in there. The Fishman BP-100 is made from piezo disks as well.
Piezo crystals are either more sensitive to bending or to pressure, depending on the orientation they were cut out of the bigger piezo crystal material.
Since piezo disks are usually made for buzzing applications, they will bend to move more air than if they would have cut for pressure sensitivity. The brass side would help bending, since it doesn't expand over length, but the thin piezo crystal does, resulting in a bending of the disk.
Theoretically a piezo foil could be in there, but they are either rectangular or a special custom order which is much more expensive than the stock shapes. But then the pickup could be bend easily, since there is no metal disk inside, only two sheets of thin synthetics. And even these are more sensitive to bending than pressure and they need an even higher input impedance (up to 22 MegOhms) for optimum load.
There are only two common other shapes of piezos I know, piezo cable (soft piezo electrical dielectric in a coaxial cable) and cylindrical rods of piezo crystal (like used in fire lighters), which couldn't have been used here for obvious reasons.
BTW, the contacts for a piezo disk are usually made at the peripheral, one to the brass disk and one to the silver coated top. Since the connection to the silver coated top is very sensitive to getting off the piezo crystal, this part is often put in epoxy to enlarge the area of contact and avoid too much mechanical stress. Now look at the shape of the pickups ...