Consider instead the case where you're a recovering gambling addict who's asked me to make sure you don't gamble again. One night I find you in the pokies room, so I take your wallet and tell you I'll give it back tomorrow morning. I agree that this is theft and possibly morally wrong; however, I don't agree that it breaches your right to self-determination, since most of the time you seem pretty determined not to gamble.
I disagree with the claim that many suicides are like that, I don't think the suicide from the article was like that, and the word "consistently" is doing a lot of heavy lifting.
Intuitively I feel that it's like two different people are making decisions about the one body, and the finality of suicide means the suicidal part of someone is wiping out the future for both, and should thus be prevented.
Again, though, the majority of suicide victims aren't suicidal for large periods of their lives. I feel that in the cases where someone is only briefly suicidal during the worst troughs of mood, the suicidal 1% of a life would wipe out the non-suicidal 99%, which is a monumental loss to inflict.
This is particularly true if they call you during the bad 1% and directly ask you to stop them from doing the thing.