Well, people had to be careful before the automobile too, you know. People could by killed by horses or wagons. The introduction of the automobile didn't make it suddenly unsafe to be in the street.
You can argue the specifics, but it seems modern recreational horseback riding is fairly dangerous. http://freakonomics.com/2006/08/28/whoa-nellie/
These things (safety) aren’t binary. Just because it wasn’t absolutely false before doesn’t mean it was much more true after.