Yes, that's definitely true. If you know a little, or a lot, about genetics, then the theory is falsifiable.

I think it still works just fine as an example though. The goal was to explain the meaning and the importance of falsifiability. Spotiswood's theory, as presented and as it was being used, wasn't making any useful predictions. No one was looking at familial comparisons, and i implied that Spotiswood wasn't making any effort to identify the gene, so the only observations that were coming in were "person lives", or "person dies". Within that context, Spotiswood's theory can explain any observation, and makes no useful predictions.

If that's not an example of an unfalsifiable theory, then it's still an example that helps explain the key elements of unfalsifiability, and helps explain why they're important.

If an audience member should then point out what you pointed out? Then that's brilliant. We can agree with the audience member, and talk about how this new consideration shows that the theory can be falsifiable after all.

But then we also get to point out how this falsifiability is what makes a theory much more useful... and the example still works because (QED) that's exactly the point we were trying to demonstrate.