I wonder if your corkscrew might be slightly bent? The diameter of the Fire Ant ferro rod is larger than the shaft of the mini screwdriver, creating a tighter tolerance.
I own many examples of Victorinox models from the older, round, mini screwdriver era and I've not had an issue using the Fire Ant ferro rod with them. This includes fluted corkscrews, and even the 5-turn ones on 108mm models. One exception is an early 70's 84mm Climber I have with fluted corkscrew that has the small clip blade. That one is too narrow down the center of the corkscrew to even get the insertion of the ferro rod started. This would have been one of the earliest models with the 4-turn corkscrew. The older 5-turn fluted corkscrew doesn't work with the mini screwdriver, so it won't work with the ferro rod.
I would say that in most cases you're safe using it with anything back through at least 1980. Just be careful and don't try to force it.