Does the NSA use Intel chips? If so, it would seem unlikely that they made their own compute infrastructure insecure.

Their mission isn't to make everything less secure, it's to make the other team's stuff less secure (where "other team" includes the citizens of the US apparently).

Furthermore, given the number of bugs in just about every piece of software (including kernels), I don't think these bugs are even an anomaly that needs an explanation. Bugs exist in every complex system, and CPUs are very complex these days.

That said, to address your direct question of "would it be possible", I'm fairly sure it would; we have hints from Linus that Three Letter Agencies have asked him for backdoors, so I'm sure large hardware companies have open channels with the NSA et. al. as well.