Thanks for the recommendations.
Unfortunately, my home do not have a real earth connection. In fact most of the main's sockets only have 2 pins (neutral and phase/live) with 127v. In my bench they are interconnected with 3 wires, so the function generator and the scope do share the same ground but, again, they are not going to earth.
I don't typically mess with higher voltages when I am using the scope, and when I do I tend to use the high voltage differential probe.
In this particular case, I was testing the bridge rectifier using the function generator to generate the sine wave and I wanted to try out the real deal with a transformer to see the differences. With the function generator, it was impossible for me to see the full wave rectified, unless I use the diff probe. I would only see one half or another, I think that is because of the shared ground. Only way to see the full wave was using scope math channel. It as an interesting learning nevertheless.