Why ask for a bug when you can just sit back and wait for them?
Yes, I'm kidding about the first part.
Since neither the threat nor the reality of PR disasters has ever given the NSA pause before, occam's razor strongly suggests this theory of yours is wrong.
I would also disagree that your assessment is correct anyhow; they are insensitive to certain kinds of bad PR, but not generally immune to it, nor do they act generally immune to it. The people in charge of funding the intelligence community may not come after them for getting caught putting backdoors in things; indeed, this may even prove to the people controlling the purse that they are doing their job. But they are certainly sensitive to ensuring that the people controlling the purse do not come off looking bad, and as a part of that, sensitive to not getting caught conducting open, unambiguous acts of war against every nation in the world. We all "know" that they do, everybody else "knows" that they do, and everybody also "knows" that you shouldn't trust Chinese-manufactured electronics either for the same reason, but it's still not openly known. The distinction between open secrets and openly-known facts may greatly confuse Spock and he may shake his head about how illogical it is for everyone to know a thing and for everybody to know everybody else knows but still act as if nobody knows, but is an integral element of understanding human politics, in which appearances matter a lot.
Given that we know that intelligence agencies have asked for backdoors before, in both hardware and encryption standards, do not interpret my post here as a claim that they would never ever even think of asking for plausibly-deniable CPU bugs to be inserted into hardware. I am just saying that Occam's Razor says we should prefer the perfectly plausible scenario I gave above where they do not have direct involvement in these bugs, not because of their pristine ethics, but because given the circumstances on the ground, actively intervening is not their best choice from their point of view using their valuation function, when they can attain all their goals without active intervention.
(I'm willing to believe in things that might be labelled "conspiracy theories"; history is rife with proof that they have existed in the past, such as the aforementioned cases where we know backdoors have been inserted into crypto standards, as well as other things such as the way in which the Soviet Union was created which essentially involved what was initially a small conspiracy, and I see no reason to believe they have ceased in the modern times. But I want to see how the conspiracy theory passes Occam's Razor; many of the conspiracy-minded, in my opinion, underestimate the randomness and everything-is-always-correlated-a-bit-ness of the real world.)