Mains rectification vs 1:1 transformer
What you are describing is an isolation transformer.

Since the mains lines are referenced to real ground, touching one wire with your feet or other hand electrically connected to ground completes a circuit with YOU in it. That tends to spoil your day.

If used properly, an isolation transformer isolates the power lines from the ground. As such, touching the live wire on the isolated side while touching ground with your other hand does not complete a circuit.

Of course, none of that matters if you touch both sides of the power on the isolated side. 

If you end up grounding one side of the isolated side of the transformer, you make that situation worse. In fact, in that case you are in more danger than touching the primary side which should be protected by an "earth leakage" or "ground fault" circuit breaker. Unfortunately, an isolation transformer takes those out of the circuit. 

The transformer does however limit how much current can be passed since it will saturate at some point. That is better than connecting your self direct to the multi-megaWatt grid.