You're right; complaint rate and similar metrics tracking were implemented by major consumer email providers in the early 00s, if I recall correctly. The technique has been around long enough for those providers to have systems in place to control for edge cases like the one you mentioned - there are enough subtle behavioral differences between an average user reporting something as spam, vs. a deliberate 'complaint brigade', in order to be able to discern reasonably well between the two - or at least, to reduce the impact of the latter. Users marking 'this is not spam' for messages that mistakenly land in spam is a key metric as well, and is part of how a lot of senders recover from short-term spam folder delivery.
Whether or not additional complexity is justified is something that can be measured in a case like this - and that's exactly what Gmail does, using a variety of different metrics, which allows them to make an informed decision about whether to take on the additional complexity cost.
Should they weight false positives for this message type more heavily in their accuracy metrics? Definitely, these are particularly critical to classify correctly.