This doesn't really answer your question, but it's kind-of related.
The quote below is from an interview on 16 July 2005
http://www.accio-quote.org/articles/2005/0...et-anelli-3.htm

MA: What about Harry's family — his grandparents — were they killed?

JKR: No. This takes us into more mundane territory. As a writer, it was more interesting, plot-wise, if Harry was completely alone. So I rather ruthlessly disposed of his entire family apart from Aunt Petunia. I mean, James and Lily are massively important to the plot, of course, but the grandparents? No. And, because I do like my backstory: Petunia and Lily's parents, normal Muggle death. James's parents were elderly, were getting on a little when he was born, which explains the only child, very pampered, had-him-late-in-life-so-he's-an-extra-treasure, as often happens, I think. They were old in wizarding terms, and they died. They succumbed to a wizarding illness. That's as far as it goes. There's nothing serious or sinister about those deaths. I just needed them out of the way so I killed them.

MA: That sort of shuts down Heir of Gryffindor [theories], as well.

JKR: [Pause.] Yeah. Well - yeah.

MA: Another one bites the dust.

I'm not following the logic here, of why this "shuts down" the theories.
Then again, I never did see a need for an "Heir of Gryffindor," or where the idea came from.
It's the bad guys who make a big deal about their blood lines. Why would a good guy know or care?