Does it matter if my newly installed GFCI reads "open ground"?
No. In fact, GFI protection is a safe and legal way to install 3-prong receptacles on non-grounded wiring.

You are likely reading a ground in some area because armored cable will show a ground with a tester but it is NOT a safe or acceptable means of ground in all cases. Only one type of AC cable will provide an acceptable ground.