In the following paragraphs, I think I understand what is supposed to mean, but I can't parse the part in red. What is "whose" in the sentence modifying? "the ability" and "Doug Gurian-Sherman says" is a inserted or transposed phrase?
In the audio version of this article, it seems to say "that groups" for the "whose".

The case has attracted attention from other groups, including the petroleum, home building and pesticide industries, that believe the environmental law has gone too far. Along with the Farm Bureau, officials of those industries have written to the Supreme Court backing Monsanto in the lawsuit.

On the other hand, the organic seed company's backers include the Humane Society, the Natural Resources Defense Council and the Union of Concerned Scientists, whose Doug Gurian-Sherman says the ability of citizens' groups to question the decisions of regulators is one of American democracy's important checks and balances.
and the Union of Concerned Scientists, whose Doug Gurian-Sherman says

Doug G-S belongs to the organization, "the Union of Concerned Scientists."

Yesterday we heard from the Boy Scouts, whose leader, John Jones, said there would be no more of this nonsense.

The issue is in the hands of the United States Senate, whose Harry Ried (the majority leader) announced that the two sides are deadlocked.

This is a common way of putting it.

I'd have to say that "whose" modifies the organization.

I'm going to sue the company whose product ruined my hair.

I 'd say "whose" modifies "company," but I'd like to hear other opinions.
Thank you for clearing that up. Now I can see the construction.