Over the past few months, there have been sporadic reports on the wrong local news showing up in Google News. One such thread at Google News Help has several comments about the issue by a Googler named Inbal.
What appears to be the issue when Google shows non-relevant local news in the local search of Google News is that Google is matching incorrectly. Inbal from Google explains, most recently, the root cause of the issue:
The root of most problems reported in this thread is bad geocoding on zipcode: some zipcode maps to the right name (like xxxxx --> Springfield, Mass), but we then think that text is for some other place with the same name. Our engineers have been fixing these zipcode related bugs following your reports, so please keep them coming!
In other cases, the searcher has entered the wrong zip code - but that is not common - what is more common is the issue above.
Finally, the last reason why the local news in Google might not be local is because there simply is not enough local news sources for your area. Inbal said, "there are just not enough news sources to show from a small town, as we may not be indexing some local sources."
Those are three possible reasons why Google News may not be providing locally relevant news for you.
Forum discussion at Google News Help.