It may have been a partial or a cue that was fitted to a cue with a smaller joint dia. That would explain the logo missing. Although, the OP did say that this did say I3 on it, perhaps he just failed to photograph that part of the shaft. Either way, I would say that this shaft is definitely an I-Shaft.
With regards to the ferrule, two thing could be the case that I can think of... The orig. ferrule could have broken and was replaced with a longer one. Or, more likely, the ferrule may simply be longer because this is an earlier I-Shaft. The earlier ones had longer ferrules on them according to a McDermott dealer in texas that I bought and I-Shaft from. This was about a year ago that I bought it, but he said he had the shaft, along with many others with the same attributes, since McDermott introduced the I-shaft concept. That's when they were doing all of the logos (I-1, I-2, I-3) above the joint collars in black paint rather than corresponding colors with the inserts.
Hope the info helps.