I've had some in depth discussions over the years about this with a few different sources. I've been told repeatedly that there was a recording problem and that the original tapes were mashed up and twisted during recording of this track, and were unusable.
Now after hearing this, I'm betting that they played the cut, the guitar was so out of tune that it was the guitar equivalent of the Weiland Vasoline fiasco (where he was saying that he wasn't high but his ears were out and couldn't sing). Rather than look unprofessional at the time, the STP camp at large let out that the recording was damaged and unusable, as opposed to placing a performance problem on their bread and butter.
Now, with time behind them, the DeLeo's don't care as much about the ego component and tell the story as it was. Or, more likely they never weaved the story in the first place, but someone in their camp did to protect the integrity of STP as a whole considering how, at the time, MTV Unplugged was the "artsy" and "validating" show of the era.
The Sin conspiracy.
Either way, if it exists it's a failure of epic proportions to have not included it with this set after all this time.