They could treat it the way that Stolen Valor is treated: if the perp receives or hopes to receive ANY benefit, tangible or intangible (including sympathy for being a poor downtrodden POC), then it is simple fraud and can be prosecuted as such. Media companies who push these stories and then fail to issue corrections (fake but accurate) and denounce hoaxers could be prosecuted for accomplice after the fact, and conspiracy.
Put a few hoaxers in jail, along with the reporters and editors who push the stories, and it'll dry up.