I installed just SSMS. I installed it on my PC so that I could connect to our SQL Server 2012 instance which is on a separate server. When I installed SQL Server 2012 on the *server*, it also installed SSMS on the server, and that is working fine. I tried to install SSMS on my PC from the server ISO, but the server ISO is 64-bit and my PC is 32-bit, so no go.

I checked out the link you provided from my PC, just in case, but it says: There are no SQL Server instances or shared features that can be updated on this computer.