BMWs are electrical nightmares. It would not surprise me if BMWs had wiring faults that caused fires.
That said, this story doesn't show evidence of that. I counted 11 separate BMW's (if you count the Mini they snuck in there) in the article, with years spanning from around 2003 to today. In those years they've sold nearly 4 million cars in the US alone.
11 cars out of 4 million is not indicative of a pattern. In fact, to find things that are less likely to happen based on this story, you have to start talking about winning the Powerball, or getting hit by a meteor.
If the "journalist" had been more interested in facts and numbers and less interested in sensationalism and Darth Vader costumes, I might be swayed into wondering if this were true. But as it stands, it's just a BS story trying to scare people into watching the newscast.
I will also point out that this is a "book" month, which happens 4 times a year. It's the period in which the Nielsen ratings company measures viewership. That measurement is used to determine how much stations can charge companies to advertise on their air. You tend to see a lot of sensationalist BS during a book month because it's a lot easier to spew out BS to draw eyeballs to your network than it is to do actual in-depth journalism.