Mac iTunes requests update, but App store says no updates available
Since the apple advisor was able to perform the download at his end, but I was not able to at my end, my suspicion was that there was a problem with Apple's content distribution network.  

This morning I tried again.  No joy.

On a hunch I tried logging in on a spare admin account.  No problem. connected to  the apple support site, and downloaded the update. Worked like a charm.

At this point it's not clear what happened, but with odd behaviour it does bring up one additional possibility to try:

Attempt the update as a different user.