True. That is a _kind_ of courage. Unfortunately, many people think it is the only kind of courage there is. It isn't so by a long, long shot.
But first, let's type on this kind of courage. I know more people that would be courageous (in the traditional sense above) for the sake of others than for their own sake. They would be regarded as cowards when their own arses are on the line yet would put their arses on the line in order to protect love ones or strangers.
One could argue that these kind of people are "conditionally" courageous. It isn't so. What's happening here is that you are looking at the demonstration that there are many different kinds of courage.
There is the courage of being responsible for a family with small children and have to tough it out through bad economic times. There are cowards that leave. There are heroes that stay even when they have to say to their children "there will be no present this Xmas either", or far worse, when there is no food to put on the plate.
There is the courage of the guy that spends his youth working and studing instead of binge drinking due to flaws of character or peer pressure.
There is the courage of doing one's job right. It is the courage of having one's standards, be you a highway cleaner, a doctor, a teacher, or an electrician.
There is the courage of loving and letting others to love you.
There is the courage of keeping one's chin up regardless of the sht storm you might be facing due to poor health or disabilities.
There is the courage of standing tall when everyone else sits down.
There is the courage of doing the right thing inspite it all.
In short, you don't need to be physically willing to fight in order to be courageous. Look around your life and you will find many instances when you've shown yourself you've got guts.
When your ego acts up dealing with people and when being overwhelmed by circumstances, remember this maxim: Your defeats will only stop hurting when you no longer celebrate your victories. Supersede confrontation. The objective of this post is to show you that there are far more important ways to define yourself than by a narrow conception of a virtue, in this case, courage.
Be courageous on the matters that actually matter. You don't need to be a physically brave in order to lead a dignified life. The most violent and aggressive will always find another others more violent and aggressive, regardless of domain.
Be constructive and be courageous in your constructiveness.