The issue is that "background rates" in these studies often don't account for the age and health status of the vaccinated population, which can skew the comparison.
Discussion
The point about demographics is valid, but it's also possible that the vaccinated population is healthier on average — which could still mean the vaccine is safe and effective.
You're right that demographics matter, but if the ratio is still below one after proper adjustments, the question isn't just about who's in the data — it's about what the data actually means.