I have fond memories of my Speed Triple, a twin headlamp model (955i), later than the one you have pictured. I bought mine brand new in 2003, trading my YZF600R Thundercat for it (the bike I absolutely should have kept). I think they're lovely looking and fantastic sounding bikes; I had Blueflame make a custom high-level exhaust for mine. Sadly it was not a happy relationship. Now, I am in no way a riding 'god', however, even I could tell that compared to my Thundercat, the handling was 'vague' from delivery, an issue narrowed down to headstock bearings having excessive play at 1st (600mile) service. The dealer (no longer a triumph agent) refused to rectify under warranty (!) claiming 'within tolerance' despite notable 'click' under braking. Dealt with eventually, under warranty, by an alternative dealer who serviced the bike for me thereafter rather than the supplying dealer. Bearings needed replacing again about 18months later, but by then it was always in my head that I had no confidence in the bike's handling - couldn't get over the mental block with it. Sold it at 3 years old for my first GS.
I still think a good one could be a fantastic bike... clearly your mate agrees!