Freedom of speech is freedom of speech, I disagree with limiting it for this, hate speech, or any other reason. There are positive and negative aspects to everything, and in general the cost of an occasional incident like this one is well worth the benefits. I do not like the idea of including "exceptions" to the right to speak freely.
That said, you have to understand that claims of commiting suicide are oftentimes pleas for attention more than anything. It's easy to look at a situation like this retroactively and say "wow, this was wrong" due to someone actually killing themselves, but it entirely overlooks the very annoying tendency of people to claim that they are considering self destruction as a way of getting attention and inspiring pity.
To be entirely blunt, while it doesn't match every situation, most people who commit suicide don't generally walk around saying "I'm going to do it", typically they are spotted by massive mood changes, ending with a degree of peace, and behaviors like giving away their worldly possessions and acting in a fashion that shows them as having little or no concern for the future. In general nobody is going to be able to stop someone who is REALLY intent on offing themselves, which is why in many cases someone who wanders around with a giant "I'm going to kill myself, stop me" sign is actually looking for attention.
There are also cases of faux-suicide, like the person who downs a bottle of pills (slow acting, and capable of being pumped out of the system) knowing that there is help nearby, or people who get into a bathtub a short time before they know someone else will be around and slice their wrists the wrong way.
As I've said before in response to other situations (and yes I know I'm liable to get flamed/trolled again) the whole Internet "an hero" schtick exists for a reason. I typically won't heckle someone who is claiming they want to kill themselves, but at the same time I'm not going to give them any attention either (speaking for myself) it takes more than a declaration of intent by some guy on the Internet who I don't know to make me take it seriously, since the guy could be sitting there with a real-life case of troll face listening to people respond and get all worked up, and truthfully the odds of that are probably greater than the person actually offing themselves.
I do however understand the reason why people get annoying enough to say "shut up and do it already" given all the attention seeking emos out there. Truthfully I have to wonder how many of the people who responded negatively in this case did so from having been burned in the past by taking attention seekers seriously before their true colors were revealed.
As silly as this might sound, my advice for those that feel horrible depressed is to take Saint John's Wort. I won't say it works miracles but it helps a bit, I tend to work it in withmy own medication from time to time (and yes I've spoken to doctors before), placebo or not (debatable) it seems to help a little, and this is coming from a guy that actually does grapple with severe depression. That's about the closest to commentary in situtions like this that I am likely to make unless I know someone more than "this guy I might see in message forums once in a while".