It's really arbitraty where you put a reference in a circuit, and if you desire to need one at all. You pick the reference, if you like, and put it where it works best for you when thinking about the circuit. The circuit itself will not even know you did this, and it will not even
give a holy firetruck care about the question if it has a reference or not.
Think of a battery powered device: It works when there is no connection to any other object, i.e. when it is not grounded or referenced. And it's up to you how you measure or think about the voltages in the battery powered device. Most times, it is practical to consider the (-) end of your battery the reference, which gives you (mostly) positive voltages in relation (reference...) to this reference. But you can also consider the (+) end of the battery the reference, and you end up having negative voltages. Note that the circuit works no matter how (and if) you define your reference.
With a safety transformer, the whole point is having no reference to earth ground. This way, if you accidently touch the circuit powered by your safety transformer (using one hand only!!!), you can't get too much of a shock (aside from bridging something with just one finger), because current coming from the transformer can only go back to the one same winding where it came from, and not close a path via ground (through your body).