The concern is that this is a generic strategy for destroying any media org you dislike. Simply locate and fund any and all lawsuits, forever. Any critical story could be libel. Any publishing of secrets could be an invasion of privacy. A weak case can be pumped up with enough money. Eventually the billionaire wins the war of attrition.
This is not hypothetical. Mother Jones was similarly attacked for publishing Mitt Romney's 47% comments. http://www.motherjones.com/media/2015/10/mother-jones-vander...
This is the very definition of a chilling effect on free speech!