I drilled the rivet and took the part out. Amazingly enough, by naked eye I could easily see that the part itself (it is plastic) had a larger diameter than the replacement part I bought. I measured it and the diameter of the end cap is about 0.4 mm (about 1/50 of an inch) larger than the spare part. I really have no logical explanation for this; I remember the part being a little tight when we bought the boat in July 2009 (when trying to turn it, it was a little hard), but as I explained above the part had been extremely tight lately. It seems like end ca[ has gotten bigger from before, but being plastic I find that hard to believe. Does anyone have any reasonable explanation? Do the tiller end caps used to bigger in diameter a year ago? Not only that, but the old part is also about 1 mm longer.
Old part is 23.7 mm in diameter and spare part is 23.3 mm in diameter. new part works great.