LOL, Right on my friend.
your electrical service is likely grounded effectively.
the issues are different, an equipment grounding conductor versus if your system is effectively grounded.
open service neutrals offtopic direction by others is addressed here:
if you still have fuses and have fused netural on your service then you'd want to address that first. If you have older style bx cable then yep you could have issues. bx cable is not greenfield conduit you arent allowed to re pull new wire through cable, you are allowed to pull wire through conduit.
old conductors werent thhn.