Eric Peterson wrote:
> You need to install the 7.3 redhat-release RPM. 

That did it!  Thanks for the help Eric.  
For the record, with 7.3 hard-coded in /etc/yum.conf I ran:

# yum install redhat-release
Gathering package information from servers
Getting headers from: Red Hat Linux 7.3 base
Getting headers from: Fedora Legacy utilities for Red Hat Linux 7.3
Getting headers from: Red Hat Linux 7.3 updates
Finding updated packages
Downloading needed headers
Resolving dependencies
Dependencies resolved
I will do the following:
[update: redhat-release.noarch]
Is this ok [y/N]: y
Getting redhat-release-7.3-1.noarch.rpm
Calculating available disk space - this could take a bit
redhat-release 100 % done
Updated:  redhat-release.noarch
Transaction(s) Complete


Then I restored the original yum.conf (changing the hard-coded value
back to "$releasever") and Yum now correctly identifies the system.

# yum check-update 
Gathering package information from servers
Getting headers from: Red Hat Linux 7.3 base
Getting headers from: Fedora Legacy utilities for Red Hat Linux 7.3
Getting headers from: Red Hat Linux 7.3 updates
Finding updated packages
Downloading needed headers
<lots of stuff>