I don't know if "solved" is the correct work, but I found out how to change it in order to eliminate the problem.
I thought after a while that the term "message" might be a reserved word - or something along those lines. This might be why the syntax "&message=123", used to identify the number of the message you wish to view, ended up giving a value of "YES" in the variable $message all the time.
So I changed the name of the variable in the links on the index page for a person's private messages (this is in "viewmessages.php" for the newer version, and "main.inc.php" for the older version that I still work with). It now reads something like "&numofmsg=123". Then on the first line of the "viewmessage.php" script, I put in this line:
$message = $numofmsg;
(instead of changing the name of the $message variable throughout the script)
I'm not sure if my reasoning is correct about why it works, but hey - it works! Even one of my users who has been having lots of problems with this is now reporting error-free private messages.
