It looks like you haven't been paying close attention to the Gawker suite: Gawker also had insurance, but Bollea strategically dropped a charge that would have let Gawker claim against insurance (and at the same time reducing the total amount he would receive). This suite isn't about damages: it's about bankrupting Gawker for better or for worse. There's nothing that suggests a similar strategy can't be employed against Mother Jones.
Plus Gawker's case was specifically structured to avoid an insurance payout. A blueprint for others in the future.
That's obviously a big problem. I have never understood why America insists on a dogmatic principle that inherently and unavoidably gives a vast advantage to well-off parties over poor parties. You can get away with a lot of vexatious litigation before the courts (a) notice it and (b) actually act upon it.
A billionaire could fund cases against a media company entirely irrespective of the merit of those cases - the media company would still be forced to pay the legal fees associated with defending themselves, even if it's as simple as just getting it thrown out of court. Do it enough times and you've bankrupted the company.
For an example, Mother Jones was brought to the brink of bankruptcy for reporting an entirely true and legitimate story:
http://m.motherjones.com/media/2015/10/mother-jones-vandersl...