I think his standards are very realistic in the sense that it's entirely possible for new media to link to primary sources for their claims or to explain why those sources aren't available in cases where they can't do so.
I further think that this would be a good norm for us to have. Don't implicitly trust claims that aren't properly sourced. I even think that we should have this norm with scientific research: if the researchers don't make their data publicly available, don't trust their claims about their research. The amount of fraudulent science happening is evidence for the importance of norms like this.
Is it reasonable to expect that news media will actually live up to these standards? To the extent that people don't hold them to those standards, no, I don't expect that they are going to live up to them. But in that case I also don't see why I should implicitly trust their claims.
This doesn't mean distrusting their claims. An unsourced claim doesn't make me more likely to think the thing is false than if the claim wasn't made.
As far as the OP, I certainly think that it's plausible that everything she said is true. But asking for people to supply evidence of their claims, even claims I see as entirely plausible, isn't harassment. It should be the basic culture on a skeptic's board. I'd actually prefer if it were the basic culture more widely, but at least we could try to model that here.