When trying to refresh my memory I Think you are right. You don't need to run the installation from both nodes, but on both nodes. As long as you run the SP installation on the Active node, the SP installation will first upgrade the passive node and then the ative node.If the passive upgrade will fail (this you can check by checking the sql server version when failing over) there is a switch you can run with the sp installation...eg spxxxx.exe /passive. This switch will just install the SP on the passive node.
A node restart is not required, but a SQL service restart is required. But as Always, I would prefer to do the node restart as you can failover the instance during the restart.
I hope this was an answer to your question and I am really sorry for the missunderstanding from my side....