Isolated Ground causes ground hum.

I'm not an electrician, but I have two ground rods installed to my house.
  There is an earth ground attached to your service panel (circuit box) which is the ground for all circuits in your house. 
  If you have a dedicated AC line, it is also grounded to your house. You may attach a ground rod to this line which has an isolated hot and neutral to your system. 

There can only be one ground for the entire house and your components must share this ground.

colin, assuming there is a common ground, in theory there should be no grounding issues using RCA cables. But not all components use the same grounding scheme, so there may be a difference in ground potential which cause ground faults. Also some RCA cables use a ground connection, some don’t. In these situations there may be hum or noise introduced.

With a SMPS the issue is noise. These power supplies can bleed noise or interference back down their power cord into the mains thus contaminating the entire system.
Some modern components are using high quality internal SMPS’s. It’s the wall-warts that add noise and are not as effective as a linear power supply.