The History Channel actually said no one really knows?
It's kind of like saying that an execution in the old west may have been done by hanging but nobody really knows for sure whether the townfolk got together for a stoning instead.
The Romans executed using a cross or cross-like implement. There is no rational reason to think they may have used a single upright pole on this one occasion, is there? (I didn't see that History Channel show but I've never heard anyone outside the Dubs question that crosses were commonly used as implements of execution in the Roman empire.