I disagree somewhat with earlier posts. Yes, "could not" has two rather distinct meanings. It can refer to physical inability, and it can refer to self-control.
"I could not get here any faster. Traffic was too heavy." Or "I could not lift such a heavy box." You are simply incapable of doing the thing under discussion.
That's very different from, "I couldn't stop eating until I had eaten the whole cake." Clearly you were physically capable of putting down your fork and not eating any more. But you lacked the will power.
And yes, some things could be in a gray area. "I couldn't stop laughing at Bob's ridiculous political views." Maybe they struck you as so funny that you had a physical impulse to laugh that you tried to control but couldn't. Or maybe you wanted to laugh.
"I couldn't help leaving. I had an important meeting." Well surely you could have stayed and missed the meeting. It's not that some irresistible force dragged you out of wherever to go to this meeting. But you considered the meeting too important to miss. I suppose this is something of a third category: Not physical inability. Not lack of self-control. But circumstances making something difficult.
And yes, fluent speakers say things like that. Another way to express the same idea would be, "I decided to leave because I had a meeting that I considered more important than spending time with you." But that would sound rude. Even if the meeting really was important or urgent and whatever activity you left was not, it was just a casual party or something, you probably wouldn't want to come right out and say, this activity isn't very important. And if the other person might think that what you left was more important than this meeting, you surely don't want to say that he was wrong.