I think the principle is fairly straightforward: if some factor exists that a (possibly imaginary) opponent of yours would consider a legitimate conflict of interest, then declare it. In other words, you need to consider what other people would regard as a conflict of interest, rather than what you view as a conflict of interest. If the journal requirements are even more stringent than this, then you still have to abide by it if you want to publish a paper with them.
In this particular case, it is a requirement of the journal
i. Disclosure of potential Conflict of interests
Authors must disclose
all relationships or interests that could influence or bias the work.
Examples of potential conflicts of interests that are directly or
indirectly related to the research may include but not limited to the
following:
Research grants from funding agencies (please give the
research funder and the grant number)
Honoraria for speaking at
symposia
Financial support for attending symposia
Financial
support for educational programs
Employment or consultation
Support from a project sponsor
Position on advisory board or board
of directors or other type of management relationships
Multiple affiliations
Financial relationships, for example equity ownership
or investment interest
Intellectual property rights (e.g. patents,
copyrights and royalties from such rights)
Holdings of spouse and/or
children that may have financial interest in the work
In addition,
interests that go beyond financial interests and compensation
(non-financial interests) that may be important to readers should be
disclosed. These may include but are not limited to personal
relationships or competing interests directly or indirectly tied to
this research, or professional interests or personal beliefs that may
influence your research. The corresponding author will include a
summary statement in the text of the manuscript in a separate section
before the reference list. An examples of disclosures is shown below:
Conflict of interest: Author A has received research grants from
Company A. Author B has received a speaker honorarium from Company X
and owns stock in Company Y. Author C is a member of committee Z. If
no conflict exists, the authors should state: Conflict of interest:
The authors declare that they have no conflict of interest.
This specification seems rather more rigorous than most journals, but it is pretty clear. It seems reasonable to say that the previous funding is indirectly related to the research in the paper in question. I would also say that all four authors of the paper being affiliated with think-tanks (e.g. the Heartland Institute) that are active in the political debate on climate change is a far more significant conflict of interest than the funding issue. Having said which, this is IMHO a fairly minor issue, which should be dealt with via due process, just like any other case. I am more concerned with scientists being harassed by FOIA requests, regardless of which "side" of the argument they support. It would be better all round if we could just stick to the science.