Why did he show her that photo?
Goodman's character was a nutjob and all that, but he wasn't supposed to be retarded. He was paranoid and didn't like to take risks.
If Megan actually existed, then why not show a picture of his real daughter? Surely he had at least a picture of his daughter?
If "Megan" was actually the girl he kidnapped and all the anecdotes were from his time with her, then why take a risk of showing a photo of a missing person? Her disappearance had made the news according to Emmet.
Sure, she was unlikely to recognize her since she was from Houston and not that rural area, but why take this risk, especially when you also have another guest who knows damn well who she is?
Plot device, I know....