Alvarez's lawyer has previously argued that the lies were harmless ones and that in many cases, there is no victim at all. Webb and Shipley said that if nothing else, the lies are disparaging to the memory of the true heroes lost in the line of fire.
Shipley, who also runs a prospective SEAL training camp called Extreme SEAL Experience, said he spends so much of his free time exposing fakers to defend the honor of his comrades. "We do it to honor our fallen teammates – guys who can no longer stand up and defend themselves," he said.
"Nothing fires me up more than running into these phony Navy SEALs and knowing that I lost over a dozen friends that sacrificed for their country and now these guys are out there trying to take credit," Webb said.
Regardless of what the Supreme Court decides, another military watchdog, Doug Sterner, told ABC News that cases of fake military heroes aren't likely to stop overnight -- after all, there's a new Navy SEAL movie coming out and, most likely with it, imposters ready to latch on to the fame.
ABC News' Vic Walter and Ariane de Vogue contributed to this report.