Did I miss something in the original report from the dealer? How many overheats were recorded by YDS?
If under 5, it's not good, but probably not abnormal. If over 5, then it would be questionable abuse if it was blatantly ignored (that would make it a judgement call. If over 10, then I would agree that it could have been a bit abusive.
That being said, if you were backed into an area where you had to run an engine to get away from the weeds, then you would pretty much be required to run plugged up with weeds a bit to get out. But the recorded overheats shouldn't lie about the fact that it was hot. I have run my own boat plugged up (no wake mode) to get to deeper water so that I could jump in and clean out. Sorry, clean out ports cannot remove huge plugs in the grate. Brag as much as we like about these clean out ports, but when the grate has 15lbs of weeds on the outside per engine, the only way to get them out is by taking a swim or Jeff's reverse trick, which works.
If I were to run these motors full of weeds and it is noticeably cavitating, then an overheat is going to happen. I have seen it on a 1.8ltr engine. That one time was all it took for me to realize it didn't take much to overheat when plugged. This should not be much different on a TR1.
As far as damage to the engine, now it's a call by the dealer, and this is where your relationship with the dealer comes into play. Has yamaha customer support been called by the dealer, or by yourself? Whenever I have had to do this with any of my Yamahas with original warranty or YES, it was a sales job by the dealer. Yamaha listened to the complaint by the owner (me) but would go back to the dealer to get their professional opinion on if it looked like MFG defect or abuse. THEY DON'T CARE AS A DEALER, they will get paid either way. So it is wise for them to play it as defect, so that they keep a happy customer.
So for the love of God, don't burn the bridge, and encourage them to call Yamaha customer support, as you plan to do so, and you want your stories to match. From what you have told of your side of the story, this could easily be sold to Yamaha as an MFG defect, rather than abuse. We don't know which is chicken, and which is egg. Why would the dealer gain from selling it as abuse? Unless the evidence is very clearly abuse, which we don't have access to. But my guess is if (like stated above) had more than 10 overheats, it would be the weak dog in the street fight.
Good luck either way.