Ride height requirements are "safety guidelines" that have been set to insure that almost nothing can happen to any rider who meets or exceeds that limit. Given the legal environment in the US, I'm sure the limit is set well above the actual point at which someone would be at risk of falling out of a ride.
It's not some magic threshold -- at 47.9 inches you plummet to your death, but at 48.0 inches you are safe and secure

There should be several inches of "safety margin" around these height requirements.
I think most rides give only an illusion of risk. Most of the true risk has been engineered out or minimized (except for people with unknown physical abnormalities). It is probably safer on thrill rides at high quality amusement parks than walking across the streets or the busy parking lots a DW. JMHO.
By no means do I want to try and talking someone else into putting their child on a ride if they are uncomfortable with it. As with most things, parents should make up their own minds based on their own evaluation of the situation, level of risk aversion, the child, etc... and also remember to be polite to CMs if they prohibit your child from riding since the CM is just doing his/her job.
My DS13 is very petite (51" tall - 60 lbs), but a thrill seeker. Until recently, she did not even qualify for the 48" rides, not to mention the best rides at Universal Studios and our local Six Flags. I try to get her on any ride she is willing to try and have done so for the last 3 years. Platform shoes are good for 1/2" to 1". Pony tails and hats and standing extra tall can squeeze out another 1/2". I always ride right next to her to keep an eye on her.