But "sufficiently-sick people go to the hospital" is always true, surely? You don't get loads more people in hospital unless loads more people are getting sick.

But "sufficiently-sick people go to the hospital" is always true, surely? You don't get loads more people in hospital unless loads more people are getting sick. A biased sample's informative if you know exactly how it's biased – in fact, it can be more informative. (If you want to study popular music, you look at the charts, not a random sample of tracks uploaded to SoundCloud.)