I think you can truly want to die but have reasons you want to stop yourself from doing it. For example, you may be aware of how much killing yourself would hurt certain people. That could cause enough hesitation to seek help. Another factor could be fear of a botched attempt that could cause permanent disability. I met a girl in a psych ward one time who had brain damage because of what she overdosed on. I'm not going to detail other ways attempts can be botched, but there are several I can think of off the top of my head.

Anyway, I get what you're saying, especially having made attempts myself, but there have been times I wanted to die just as much but didn't act.