The basic idea about the "radio DJ reports on what you've been up to as part of the news" is a good idea. It makes sense that there would be radio (since fixing up the tech here isn't too hard), and it makes sense that there would be news on the radio (since people want to hear what happens). It even makes sense that activities the player engages in are part of said news.
Like most things about Fallout 3, New Vegas fixes it. In this case by:
- Not intimating that the broadcaster has personal knowledge of what you did, instead of simply reporting what witnesses are saying.
- Restricting to things that would plausibly have witnesses.
- Not making the entire thing about you, since you know what you did (I mean, if Moira writes a book, the report should be about Moira not the PC, no matter how much you helped.)
- Avoiding praise or condemnation of the player character specifically.