That is true. If a person in danger of hurting themselves or others they are (usually) admitted immediately but there is bed shortages which means desperate people can be turned away at times, or discharged too early. Many suicides have been documented to be preventable if only the public system worked better. Then there is the long waits to see a psychiatrist and it is much more difficult to shop around and find one who suits you, or is at least helpful. Saying that I have never been turned away from a public hospital when suicidal (this happened about three times and 5 times after an overdose) but I did have to wait in emergency for two days, under close watch before a locked ward bed was available.