Mach,
You are correct. You must possess a valid company ID that has a recip agreement with the company you work for. In addition, you must posess a current medical and license.
If you are caught, the FAA will suspend your pilots license and you could face jail time enforced from the FAA and the TSA.
Impersonating a pilot employed by an airline can also get you on the TSA "No-Fly" list.
Regards,