I'm pretty sure most clinical psychiatrists have the training and experience to know that many suicidal individuals conceal or lie about the extent of their ideation. It follows logically that they understand there's little they can actually do in those cases. They will usually know when someone is lying to them about the extent of their problem, but there's little they can do if they can't get them to be honest. They have limited options for people with real intent, either admit them to a ward or prescribe strong anti depressants; which most patients are trying to avoid.