The article posts a situation where Conservatives and Labour have 270 seats each, Lib-Dems 30, SNP 40. And one of the options it gives is a LD+Lab+SNP agreement - to which he then asks
"...what gives Ed Miliband the right under this scenario to be prime minister over Cameron?"
To which my instant thought is - "The fact that he can command the majority of the commons." If he has the Lib-Dems and the SNP behind him then he commands the votes of (in your example) 340 MPs (at least for the budget and votes of confidence, one assumes). That's enough to make someone Prime Minister.
If you don't believe that - if you don't believe that the votes of all MPs count when choosing the prime minister, irrespective of their party, then fundamentally you don't believe in proportional representation and coalitions, because that's going to become _more_ important and common under any PR system than it is under FPTP.
We could see a government elected, under PR, made up of three parties each commanding 20% of the vote, against a remaining party consisting of 40% of the vote. And that would be completely right and proper, because they would be representing 60% of the population, and therefore their choices have a democratic mandate.
"Largest party" is an irrelevance. "Largest block of support" is what matters.
*In fact, this post started as a comment on it. Which does't seem to have made it through the filter for some reason. I'm going to be charitable and assume that it got filed under spam.
Original post on Dreamwidth - there are comments there.