I would not regard that comment on the Apple forums as tacit approval. It sounds like they're just trying to decide if some additional BSD APIs should be added for use in iOS apps.
In general, if there isn't an iOS header available for a function, then it's considered a Private API (for example, something under https://developer.apple.com/library/ios/
). The official policy on Private APIs is that they're not to be used in apps distributed through the App Store.
Now, you can certainly use them for personal/hobby apps, or apps that you deploy in-house (Enterprise Distribution).
If the APIs you're talking about are APIs that are publically documented for OS X, and you can get them to work for iOS by copying headers, then they're probably part of the Darwin source base. It's very likely that they'll continue to function in future versions of iOS, although that's not guaranteed. Of course, nothing is guaranteed (really), as public APIs get deprecated, too.
Then, there's the issue that not all review checks are automated (I don't work for Apple, but can deduce this from things I've seen get through review). It isn't that unusual for apps to be approved with Private API usage, although if they get popular, Apple frequently pulls those apps from the store within a couple weeks. The review process isn't perfect.
So, my answer is that if you're submitting to the app store, don't expect copying in headers to work.
P.S. If you can tell us specifically which BSD function you're referring to, we might be able to give you a better answer.
P.P.S. The answer you link to about Route.h is from Grant Paul, who writes quite a bit of non-App Store software.
Additional useful information on Private APIs and the App Store