I say it depends. Realistically, some people are in too much shock to appropriately respond. So even if they want to save, they may find themselves unable to. It also depends on the method, as I could reverse an OD with Narcan but definitely not undo a gunshot to the head.
If I saw a stranger acting weird near a bridge, I would personally avoid because it could be anything ranging from a suicidial person to someone ready to mug me.
If it was my friend, who is intoxicated with substances that made them impulsively attempt to CTB, I would try my best to save them, even though I'm a hypocrite and want no one to save me. Even if they weren't intoxicated I would try. I think it's mostly because I can't handle the guilt. The "what of I could of saved them" trauma echoing.
We can say all these things about letting people die or help them in hypotheticals, but to save them would be an action we would do on impulse when the right circumstances are met. The Internet can sometimes make us null to IRL crisis situations.