I think you are right to be skeptical and I don't claim to have an insight into how accurate it is. However, mind that while Turkey is culturally about 80% western and 20% non-western, it's really unpredictable where that 20% shows up. For example, the reason the census count can be reasonably accurate even in the adversity of undocumented immigrants is that Turkish police can walk up to anybody they see as suspicious on the street and ask for their TCKN / ID to do a spot check for arrest warrants — decidedly free of the need for the western concept of a 'probable cause' or anything like that, it's a member of your community asking to validate your ID. Since they have the readers attached to their mobile phones, the check takes a couple seconds.
This also, by design, makes it really hard to be undocumented in Turkey. There's a significant skin tone difference between people from the Middle East and those in Istanbul, and the police does absolutely use this to be more scrutinous if you're even just walking by them. From an US perspective this is discrimination, and it definitely is, but this is how it works — and they're pretty good at spotting non-Turkish people. As a real example in action, there was a recent directive that required refugees to keep their residences within the borders of the first municipality they registered in (many of the Syrian refugees had moved to Istanbul from where they first registered for benefits), and the police managed to significantly clamp down on unregistered immigrants fairly quickly and send them back to the cities they registered to.
In this specific case this was the right move since the resources are allocated to states (ils) based on where refugees are registered and Istanbul alone does not have nearly the capacity to house that many refugees. My point is that Turkish police does have a lot more leeway than the US police before it becomes socially unacceptable — and while this is overall not a great thing (loose oversight), it also makes them much more effective at making a census in the right ballpark.