Most of their supported machines (including at least a few of the Thinkpads they support) look like they can't be flashed "online" from the OEM firmware. For that hardware, their documentation says you'd have to disassemble the machine and flash the firmware externally.
Obviously, this requires specialized hardware, but it's not completely insurmountable if you're really determined to run the thing.
The laptop repair shops I've seen in Shenzhen offer a BIOS reflashing service that involves using a long cable with a small clip on the end that connects to the BIOS chip. They usually reflash to OEM, to fix "hard bricks", but might be willing to flash an image you provide.
Obviously, this requires specialized hardware, but it's not completely insurmountable if you're really determined to run the thing.