Cluster-Aware Updating Readiness "Errors"

I have a two-node Windows Server 2012 failover cluster.  The Windows firewall is disabled on both nodes.

When I log on to one of the nodes (bcs-vmhyperv2), and run the Cluster-Aware Updating tool to analyze the cluster readiness, I receive this result:

When I log on to the other node and run the tool, I received the same two errors.  The problem computer is always the local computer.

I know that PowerShell remoting and WINRM are enabled!  So, the "resolution" steps don't help.

Here's proof:

If I log on to a different Windows Server 2012 system (not one of the cluster nodes), and run the tool, I receive no errors:

In fact, I setup CAU and used it to apply the latest set of Windows Updates from the third computer.

Why can't I use it from the cluster nodes?  How do I fix it?

-Tony