Is the Labour leadership election decided by the media?

In a word: No.
Now for the long answer...
Recent commentary has asked whether the Australian federal election and the present Labour leadership election may support the allegation that big media and their hired journalists are essentially picking and grooming the winners. But real life is never that simple.
Candidates for public office actively use exposure in the media, especially TV, to get their messages and personal imagery across, just as much as the journalists use the political 'theatre' to boost their careers and their employers' channel ratings. There is an 'unholy alliance' between reporters and politicians, as the former seek to raise their reputations as 'ballsy' makers and breakers of news stories, and the latter seek to raise their reputations as power-brokers who never put a foot wrong. It's a high-stakes game for both parties.
Pity the poor voter, then, who has to interpret the posturing, the half-truths and the (often cheesy or trite) narratives that emerge from this scrum, and to make a supposedly 'informed' decision based on that. To add to the complexity, the voter is provided with polling data that can influence choices by indicating who has – and who hasn't – got a chance of winning. Is there not a risk that, because the media-pack have their knives sharpened to gut one candidate, while preparing a love-fest with another, that public (or party membership) opinion will be easily swayed accordingly?
What this doesn't account for are two important ingredients: human disorganisation and competitiveness. That is, while reporters may be better informed about the candidates than the average member of the public, they are scurrying around in a relatively chaotic way, trying desperately to manage their own lives and meet deadlines, so that they really have little time to think intelligently, let alone to organise a conspiracy. And, just as one news agency and its star reporter may be doing a hagiographical job on one candidate, they then provide a competing agency and its hired hands with a golden opportunity to burst that bubble by 'digging up the real dirt' that others had overlooked.
So, the so-called 'news' that emerges is just story-telling and fabrication, but it kind of works provided that the democratic system more or less requires the candidates to be accountable for at least a few of the rash promises that they made – and there can be no doubt that rash promises abound in the Labour leadership contest!
My advice is to throw out your TV.