Depends.
The factory grease back in the day was "Campagnolo Special Grease" which was an extremely resistant material that held it's properties for a very long time. I've never been able to find out from the factory who made it or what material it was. Some information, there just doesn't appear to be a readily accessible record of.
These days, there are two greases that Campagnolo regularly use in hubs. Kluber NB52 (which may now have given way to Kluber NBU15) and Kluber PolyLub GLY 501. The latter is a heavy duty Lithium grease and is better suited to ratchets such as those in the cassette body mechanism, probably not relevant in your hubs.
The Kluber NB52 (Isoflex Topas, to give it it's full name) is a Barium soap synthetic grease with really good mechanical properties, once in hub assembly, it retains it's (synthetic) oil fraction very effectively and provides both lubrication and corrosion resistance for, literally, years - I have hubs lubricated with this 5 or 6 years ago that haven't been opened since and are still in regular use, with no loss of the buttery smooth feel, for which Campagnolo bearings are well-known.
My experience is, if the bearings are still smooth and have a small amount of stiction that tells you that the grease is still in a good, viscous, oil-bearing state, I'd leave well enough alone, until the start to get a little too free for comfort - at that point I'd strip them out, clean everything thoroughly, replace the balls with 25-Grade and regrease with either Kluber NB52 or NBU15 ...
You are right, oil can be injected through the port (in some designs of Campagnolo hub, grease could also be forced through this way but you end up with a hub full of grease). Oil will run the grease out but there's no real reason why hubs can't run on oil - the main job of the oil is corrosion resistance rather than lubrication (although it does have a job in that respect, especially in loose bearing hubs), so grease is mostly used for convenience to hold the oil where it's needed.
BITD when I worked with teams on a regular basis, we'd run the time trial wheels on sewing machine oil, ditto track wheels - replacing it with a very light "swipe" of grease if the weather was poor (no need on the track wheels, obviously) ... in that case, though, maintenance was our job, rather than our pastime, so labour time wasn't necessarily our first consideration. For practicality's sake, simply running your hubs on grease is probably a better proposition :-D
