I agree with you and I don't think you are being insensitive.
I think it comes down to if someone is being genuine or not.
A lot of them, their job is to seek attention and get attention.
They are trivializing something that is a true burden and already stigmatized by the general population, making struggles for people really dealing with a problem struggle that much more.

Those throwing around terms and really not trying to get better are different than those that really struggle.

Genuine people can help bring understanding to those that don't deal with the challenges of mental health struggle.
I love Robin Williams the more and more I learn about him. He was a really genuine guy and really felt empathy for people because he had his own struggles.
Someone like him can give reassurance that these struggles are really tough and even money or fame can't buy your way out of the issues.
It really is that hard to cope with.