You need a video OUTPUT from your TV tuner to go to the INPUT on the Slingbox. This is why they are used as a source.
Your TV will likely only have inputs. So it will be incompatible with your Slingbox as a TV programme source.
Your Sony TV will display what is on your Slingbox if you connect it to the Slingbox outputs and if you have a source going INTO the Slingbox.