I think that's the issue; we know that they must
block the flow. Notice that I did not say that they
lessened the flow, which has been disproved by the aforementioned mathematics, and which is a very different situation.
When
@pagrey did all the math awhile back I thought about what he was saying for a long time, and I realized that either I wasn't understanding something, or that the math was incorrect...and I didn't suspect the latter to be the case. So, I did what I usually do when I don't understand something: I took it to an extreme version of the concept at hand and tried to see if it made sense. Thus, I envisioned a single-slot grille opening, with the remainder being blocked; according to the math the airflow through that single slot can be the same as with seven slots if certain conditions are met...but that doesn't mean that the cooling system will still work, because that latter part is a separate question.
To that end: we know that if you block the airflow to a radiator it becomes less capable of cooling because it cannot do what it is designed to do - that can be proven with a piece of cardboard - and we know that there
must be a tipping point where it can no longer cool the engine...so if we're really talking about whether or not a change to the grille can cause overheating, it seems logical that we have to ask "what level of grille blockage would cause the radiator to become problematically inefficient?" Seems like that could also be roughly discovered with a few pieces of cardboard, now that I think about it.