I'm not so sure. The Australian has made a loss for years and years. Pretty sure Murdoch uses it for a political platform in a lot of ways. Trying to "frame the debate" and so forth. What you've said applies to the tabloids though I think.
In framing the debate it becomes a loss leader. He might lose money on the product itself, but through its lobbying power-slash-influence it gains money in other ways.
http://www.abc.net.au/news/2015-08-04/foxtel-launches-legal-case-to-block-piracy-websites/6670780
Certainly not surprised, though I guess given how much the copyright industry pushed for this I am kind of surprised they have not lodged any yet. Figured Foxtel would have done so on day one.
Case in point