I have seen stories of people defending themselves on the news. However, such stories are relatively rarely on TV, as they are not usually very newsworthy. Typically, such stories will be on local news broadcasts, if they are on TV, as they tend to be local news stories rather than stories of national importance. They also don't bother putting on the news every story of someone hurting themselves (or others) with a gun, either, which they would probably want to do if they had a strong anti-gun bias. Such stories are too common and too local to generally make national headlines. Exceptions, of course, occur when a famous person is involved. For example, when the Vice President shot someone accidentally. That becomes newsworthy not because of the story in itself, but because of who was involved in it. It would also have been on the news if, instead, the Vice President had defended himself from intruders with his shotgun, again, because of who would have been involved.
Right now, one is much more likely to see a story on the Supreme Court case involving Washington, D.C., as that is a story of broader importance than what happens in one person's house. (I do not mean to trivialize what happens in one person's situation; I am only saying that it typically is not such that it is as newsworthy for others as cases involving broad laws.)
If every story of someone defending themselves or others were on the news, and if every story of a gun accident were on the news, it would not be worth watching the news, as too much of one's time would be wasted with stories that have similar recurring themes, and they would each of them individually not have much importance in the lives of most viewers. Also, many stories that people tell are fabricated, and it would take a great deal of time to research them all to find out which ones were real and which ones were exaggerated or fake. And in some cases, one would never know what really happened, as there would not be enough physical evidence to make a determination.
But, again, the bottom line is that an individual occurrence, no matter how important to the individuals involved, is typically not very newsworthy.