The Statistics for People Who Attempt to Kill Themselves are Most Likely Grossly Inflated

First off, where do they get the figures? Well, I'm not sure but it would seem the only place would be from the triage sheet, or something similar.
Obviously, anyone who makes an attempt to kill themselves or who claim to be suicidal, comes to the emergency room. Normally the first person who they see is a nurse who gathers information: why are you here, any allergies, taking any medications, any health problems, and so on.
So, you might ask, what constitutes a suicide attempt or what does it mean if someone says they're suicidal? On a most likely daily basis, I would imagine that larger hospitals have folks come in with scratches or superficial cuts in the wrist area who claim, they tried to kill themselves. Is it reasonable to assume that they did try to kill themselves? Nope, with a few exceptions.
If someone actually plans to kill themselves and have never cut on themselves before, it's possible that the pain that's caused when they start to cut, stops them. Yes, it's possible that they want to be dead....and merely stopped because of the pain. There are few folks who fit in this category....few. However, when someone in this category can be identified, they may well pose an imminent danger to themselves.