Kurt Ullman writes:

So, if they care, they would find out who is running the flight and
stay away.

If they knew that there are substantial safety differences--but they don't.

Most of the websites I have looked around on tell you at
least the aircraft and mostly the carrier if it is other than the
airline itself. If anyone is interested all they really have to do is
stay on equipment from Boeing or Airbus and they should be with the
"real" airlines.

They don't try to look it up because they don't realize that there's a
difference worth checking into.

I agree that staying with Boeing or Airbus aircraft is usually pretty safe.

And yes, I have canceled flights myself after discovering that they would be
flown on regional turboprops, although it wasn't just or primarily because of
doubts about pilot competence.

That Dateline, USA Today, the NYT, the AP and a multitude of other
sources point out from time to time.

They talk about accidents, but not safety.

An accident is the result of an accumulation of many individual errors. Often
these errors were made for a very long time individually until they finally
combined in an unhappy way. The documentary even points this out.

Because of this, you can have two carriers that are vastly different in their
safety levels without any difference in accidents (until the above happens).
One might have very generous safety margins (and will thus avoid accidents),
while the other might have very thin margins (and will thus have an accident
sooner or later). You don't really know until the accidents occur; the best
you can do is infer from what you do know. Deep discounts on tickets are one
sign that there may be shortcuts taken on safety.