After looking over the article you linked, it seems like inhaling nitrogen could be dangerous because:

• a doctor said it could induce nausea and choking on your own vomit. When asked for sources, he countered that there was not enough research on the topic.
• a priest said so
• the gas might escape the tubes, therefore those around the gas might be at risk - valid point, to which I would suggest everyone leaving the room and/or wearing oxygen masks

??

The process of capital punishment is already morally objectionable enough. The original article isn't about that, it's about assisted suicide. And tbh, I think the US needs to figure out first how to not kill people who don't wanna die, and only then tackle assisted suicide. Let your politicians prove they care about rehabilitation and preserving life. Until then, you're asking the wolves to make laws (and choices) for the sheep.