This theory fits some lines better than others. It's not a perfect fit, but it doesn't require Dumbledore to have lied. Even if "born to those who have thrice defied him" refers to the Peverell line and Death rather than to Lily & James and Voldemort, the "born as the 7th month dies" certainly does refer to Harry's birth and Lily had a hand in that. So she's mentioned in the prophesy and would be able to hear it under either interpretation