1) From a security point of view, put yourself in the shoes of the other states. The NSA and its friends have a well proven history of backdoors and state-sponsored malware. From the Stuxnet/Flame family to the backdoors that were found on the hard-drivers malware (Story was on HN recently, I'll try to find it). So it is very normal, and as a matter of fact I'd say it's abnormal for a government to take a security product that holds administrative rights on the computer, without first inspecting its code to verify for backdoors. There is no such thing as a better state. I read on the comments "politically charged states". Well from the point of view of a Russian, the US is a politically charged state. Keep it relative ladies and gentelmen.
2) I've read people complaining about how "the way they scan"/"the way they do the detection" will be compromised. The way the AV software works IN GENERAL doesn't differ from one another. From a binary of the software one can identify with "relative ease" (for threat actors who are sponsored by governments), when the unpacking happens, decompression happens, sandboxing, hashing blocks, etc. As for the parts that are unique to the AV, for example watchdog parts and heuristics, these can also be reverse-engineered or just obteined through classical spying etc.
So all in all, source code reviews are, in my opinion, a very necessary thing. Because frankly if a simple source code review is going to fundamentally break your AV software, there has to be something wrong with that product. Because setting aside the government looking at the source code, hundreds of devs have already looked at it.