According to Olaf :
I think it's odd that the gfci would trip in this situation anyway. They are
pretty sensitive, and if there is a path for the electricity to flow through
the ground to the neutral it will to some extent.... it would seem. Which
should trip the gffi.

It would, if the ground was continuous back to the panel. It isn't in a GFI
in a groundless circuit. Which is why the NEC/CEC _insists_ that you
don't connect the ground prongs of outlets downstream of a GFI on a groundless
circuit to _anything_ (especially including other outlets).
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.