After lots of back and forth with Customer service, I finally found that a
phone's ability to send and receive text messages can be turned off by VZW.
I also found that via "my account" on their website, you can register each
phone with "text.vzw.com" and set "preferences" for texting.  Under the
heading of "text blocking" you can control the following:

Keep unwanted messages from being sent to your handset from specific e-mail
addresses, domain names and websites.

Message Blocking Preferences:
Block all messages sent from e-mail?  Yes  No Block all messages sent from
the web?  Yes  No Allow messages sent to my Nickname@vtext.com only.  Yes
No

The issue I and others have, is that we wanted to be sure that setting these
preferences to "yes" would not prevent subscribed to "alerts" such as "Amber
alerts" from reaching our phones.
Sadly and pathetically, VZW customer service is clueless. This is not to say
that they can't answer this question, but that each rep gives a different
answer, usually completely contradicting each other. They also say there is
no way to test this system. In my opinion, there should be no reason that I
can't subscribe to text alerts and still set preferences to deny unwanted
web and email based texts from being sent to my phone. As a text I
subscribed to weather alerts, while having my preferences set to deny web
and email based texts from being sent to my phone. They worked just fine. My
guess is that all subscribed to text alerts will work regardless of the text
preference settings, including Amber alerts. Anyone with any additional
information on this would be welcome to share it.

RBM