Theodore Edward Stosterone wrote:

And why is it that a private company is paid to patrol a public
beach?

The news story I just saw said that the beach he was hired to
patrol is a PRIVATE beach.

Wrong.

It was a public beach.

Some people came over to the life guard and said someone was in
trouble. He followed them over to an area that was signed as
"unsupervised area" that was a couple-hundred feet beyond his patrol
zone. The guard may not have known initially they were taking him over
to that area when they went to get him.

The city that hired the life-guard company issued a statement that they
value the life and safety of everyone on the beach regardless what part
of the beach they're on.

The lifeguard company is well within it's rights to limit
the employees' range (and liability) to the private beach.

Again, it wasn't a private beach.

And if the guard didn't respond to this guy (because he was outside the
zone) and if they guy died, then the family could or would probably sue
the city and the company for negligence or "wrongful death".

It's simply not smart to put people (life guards) in situations like
this, but this is par for the course for you Americans.