Actually, I was talking about assisted suicide being part of a public policy, as in supported by law i.e., public clinics. Nobody lives in a libertarian vacuum.
There are people who are in a state that they cannot kill themselves, they need assistance. Therefore, buy definition it becomes someone else's business. However, what happens when the wishes of the "infirmed" are unknown and someone else decides, that is also someone else's business.
Terri Schiavo NEVER made her wishes known in a way that previous judges would have allowed. There was nothing in writing. All that was ever presented was the word of her husband -- and this was YEARS after her condition developed. This was from a man who could in the best possible light be described as estranged from her, but was, in actuality, quite possibly responsible for her condition. Would you consider this to be "nobody's business"?
The eugenicists in Nazi Germany were able to murder millions of people who they deemed no longer worthy of living. They got away with it in large part because the "unaffected" adopted the attitude that it was "none of our business."
When it is a matter of life vs. death and good vs. evil, to adopt a utopian libertarian attitude that it's "none of my business" is actually to take the side of evil. There are many who say that the atrocities commited by Saddam in Iraq or the Taliban in Afghanistan never really affected the United States; that they may have hated us, but they never really threatened us. That we shouldn't be there, that it's "none of our business" -- in fact, this is the declared position of the Libertarian Party.