This is just personal opinion, but I'd think it would depend on why you're seeing someone in the first place. There's the "here and now"/"recent situation" type of stuff that someone may see a professional about because he's having trouble dealing with something and hopes to feel better somehow. Then, though, there are things like people who, say, get fired from every job because they fight with "everyone"; and someone like that may want to understand why, or at least how to deal with his/own behavior. I'd think the former kind of situation would not require a "life story" because just going back to, say, the "edges" of here-and-now situation would probably lead farther and farther back into the "story" (and maybe only need to go back x amount anyway).
With something like the latter example (in which it's more obviously the person who needs help, rather than just needing help with coping (for example); I'd think the mental health professional should be the one to take the lead with regard to how to approach a visit.
Again, this is just a personal opinion; but I do think that even in a situation like the "here-and-now"/"recent past" type of thing, rather than thinking in terms of "telling your life story", maybe a different approach would add information for the professional, and that might be a nutshell version of any other "players" in your recent/most immediate circles/life. Maybe professional would know enough to ask for that type of thing; but I think it's important (if they don't, or even if they do) to make sure to get that "context" information to them.
I'm guessing some people may tend to overlook what they don't think "would matter" to the professional who is dealing with them.
As far as whether someone understands goes, I think it's a matter of whether you want/need to just feel like someone else understands you and how you feel (in which case, that's one thing). Or, is it that if the person who doesn't understand your situation he/she won't know how to appropriately try to help.
On the other hand, leaving out whole chunks of major information isn't likely to your getting the right kind of help. People have to watch out for "that was then/this is now" thinking with stuff that went on when they were kids/teens and that may have, at least indirectly, but maybe directly, brought them to where they are in that "here and now". They may see some things as "ancient history" and think they don't matter when they do/may.