Yeah, I've noticed that, too. When I was a teen, my parents took me to the ER due to an overdose on pills - suicide attempt. I saw my father deny that it was a suicide attempt, noting that I just "forgot" how many aspirin I took over the course of a few hours (more like 5 minutes). BTW - aspirin OD, not an effective method to off yourself

But if you want cry for help, you can't get much safer than that.
Yes, I've denied suicidal thoughts as an adult 'cause I didn't want to be dragged away by men in white suits. In college I had an emotional discussion with my resident assistant (RA) and then went off to see if anyone would get a pizza with me. I asked all my friends individually, but none of them were in the mood, so I went on the second floor and got a male buddy - who I normally don't hang out with - to order a pie with me. So we're kicking back, chowing down, and I'm feeling good by not talking about my problems. Suddenly my flaming friend M. charges in, grabs me and says, "Are you okay? We've been looking all over for you!"
Turns out my RA overreacted and told university staff about our conversation. I had mentioned that I was suicidal as a teen, and they jumped to the conclusion that I was about to off myself again. Despite my assurances to the contrary, I was forced to go to an ER - again! - and get clearance from a p-doc there. Lots of waiting, hanging out with the wounded and the drunken who received their wounds while inebriated, etc. P-doc was rather ineffectual and put me through the battery of tests even after I told him I was fine.
Lesson learned - take a look at who you tell about your thoughts, past or present. If you don't trust or relate to them very well, find another p-doc or friend who will listen. Not all docs will jump the gun on committing you or assuming you're a danger to yourself. Best to tell them early than to wait until after you've devised an intricate plan.