Actually, unfortunately, this isn't true.

Suicidal ideation is quite common, but it's a long way from thoughts to actions. While suicidal ideation is itself concerning, it doesn't make someone automatically suicidal. When we do a suicide risk assessment we look at things like mental health conditions, plans, protective factors, access to means, prior attempts, family history etc. We use all of this to determine if someone is at a risk of committing suicide ("suicidal") or simply at the step of suidical ideation.

Of course, suicidal ideation alone is enough to trigger further counseling and support, but it's not enough to say someone is suicidal. You're right that these thoughts (or "seeds" are too often overlooked) but to say everyone who's thought of the concept of suicide or getting away is suicidal is similarly dangerous. We know from quite large bodies of research, that the more we normalise suicide, the higher rates get. Teens who've been close to people who kill themselves are more likely to also kill themselves, even when we correct for mental health issues and other risk factors. When the media reports a suicide as a "successful suicide" we get much larges spikes in suicide rates than if it's simply reported aas "suicide". There are fairly complex concepts, but understanding and using them gives us more weapons in our arsenal to fight suicide and suicide attempts.

Hope that makes sense.