Unfortunately, that single line addition means that this code can't be used with other open source projects. It can't be combined with code released under the BSD, MIT, MPL, GPL or other OSI-certified open source licenses and kept under the same OSI license. This puts it more in the 'shared source' realm than the 'open source' realm.
The GPL forbids additional restrictions on code, so you can't legally combine something that is GPL with a restriction like this.
Adding something like this (that we'll call Apple BSD) to anything that is MIT/BSD would end up being Apple BSD, because you'd have to ensure this restriction is applied to the resulting product, over an above MIT/BSD.
As for the GPL, I think you missed section 7 - "Additional Terms":
Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms:
e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks
It's incompatible with BSD/MIT in the sense that whatever you combine with this Apple-variant BSD becomes Apple-variant BSD and can't be straight BSD or MIT anymore. In that respect, GPL code is also compatible with BSD/MIT as it can legally be combined, it just becomes GPL and can't be licensed as BSD/MIT anymore either.
As for the GPL notice, I hadn't realized that was added in GPL3, so these additions by Apple would be allowable under GPL3. I don't use GPL3 so hadn't known about that, thanks for the heads up. They wouldn't be compatible with the more-popular GPL2 (Linux and everything else), though, which has no such allowances.
If anyone's wondering, the GPLv2 is slightly less explicit: it doesn't directly state that it's strictly a copyright license rather than involving trademarks, but it's strongly implied, and has been treated as such in court, e.g. this from Germany:
Correct, this is one of the few restrictions GPLv3 allowed.
But this text does not exist in GPLv2, so it may or may not be considered GPLv2 incompatible (I don't remember the FSF's last position on these clauses, because almost every other license that has them is gplv2 incompatible for other reasons)
