How critical is the "Environment" in the NIH grant application?

Just how critical is a supportive “Environment” to the successful conduct of a research project supported by the NIH? As construed in the current review criteria, this criterion comes at the end of the list. In my own experiences reviewing so far (mostly under the old criteria; the new scheme has only been in place for two standard rounds of review) the Environment is almost always found to be “highly supportive” or some such. The only consistent variation from this has to do with investigators who are more transitioning than established. In those cases I have had reviewers tell me at times they mean criticism to be a help to the applicant, a prod to the institution to support the PI a little better. Every once in awhile, however, there can be issues in a specific proposal that put the focus on the Environment and the support of the University for the PI.
A provocative comment and my own response triggered these musings.

Now before we got too far down the road, let us review. Despite the way we talk about things in this business, including here on this blog, the NIH grant is not submitted by the PI nor is it awarded to the PI. It is submitted by, and awarded to, the local Institution (University, Research Institute, company, etc).
[ Sidebar: This notion is reinforced by the Conflict of Interest rules in grant review which appear strange to new reviewers. The most hard line conflict is with the University/Institution- if you or your family members work at the place the application has been submitted from you are in conflict. It doesn’t matter that it is a huge University, you don’t even know the PI in question, the field is pretty far from your own…nor that you kid works on the groundscrew and can’t possibly have any real benefit from your positive evaluation of that grant. In contrast you are not in automatic conflict with your best science buddies who work halfway across the country. ]
Given the technical definition, one might think that in reviewing we would be very much focused on the University/Institution. I find this not to be so and in fact the focus is very much on the PI. On the face of things anyway, see below for more. There is a natural bias to this, of course. The reviewers ARE PIs and they operate in this convenient fiction in which they think of the grants are “their” award. They think of themselves as a representative of their owndamnself first and as a member of their University second (if at all) when it comes to grant matters- so why should they view an application any differently?
Commenter David appears to be suggesting that it is time to shift that review balance back toward the “Environment”,

Any institution that prostitutes its research program to the highest bidder should be ashamed of itself, and the NIH should consider whether to review future funding to such institutions in light of these unfortunate choices. Put differently, if an institution is not willing to support NIH-funded projects carried out in accord with the academic freedom of its researchers, its participation in future funded research projects should be viewed critically. I hope that every study section member who reviews an OSU grant considers their rating of the “Environment” a little more thoroughly in future years. While ones wants to avoid punishing the hard-working scientists at OSU for their institution’s behavior, a clear and unambiguous message must be sent.

particularly in cases where the University has pulled some shenanigans that we (as a scientific community) don’t like very much.
I should point out that this is not theoretical, I can remember maybe 3-4 grants that I’ve seen come through study sections I’ve attended where something like this arose. Details differed but the essential component of “do we punish this PI for the clearly adverse moves of the University” was present.
This is also not theoretical because we already overtly or covertly punish some PIs for selecting the wrong institution to hire them. Right? PIs who come from smaller, less research-intensive Universities are less likely to submit the larger and more ambitious proposals. If they do, they start to take fire for feasibility (which in these cases depends on the type of Environment, even if not directly stated). One way or another the support Environment shapes the grant destiny of the PI.
So is it any different to criticize an application because of a recently changed attitude on the part of the University?