Here’s an issue that I can see with a bootleg-grounded GFCI (or any bootleg grounded receptacle):
Yes, even a bootleg-grounded GFCI will protect a person against a ground-fault shock from an appliance* plugged into* it or *downstream *from it.
However, with a bootleg ground, the current returning to the panel via an unintended path, (external metal parts of wiring, such as metal junction boxes, cable armor, cable fittings, etc.) can create an unsafe condition around those parts, such as arcing (which can result in a fire) or voltage differences that can result in a shock.
And, since those conditions exist upstream from a GFCI receptacle (between the receptacle and the breaker), that receptacle cannot detect a fault on that part of the circuit.
Long story short, a GFCI with no ground at all is much better than one with a bootleg ground.