It incurs some cost, but whether it is higher is very debatable. This is very much workload dependent. A smart compiler can elide most reference updates.
Apple's ARC is not a GC in the classic sense. It doesn't stop the world and mark/sweep all of active memory. It's got "retain" and "release" calls automatically inserted and elided by the compiler to track reference counts at runtime, and when they hit zero, invoke a destructor. That's not even close to what most people think of when they think "gc". Of course it's not free, but it's deterministic.
I agree with you that most people tend to associate GC with something more advanced nowadays, like mark and sweep as you said in another comment, but it seems pointless to argue that ARC is not a form of GC.
This Apple marketing meme needs to die. Reference counting incurs arguably more cost than GC, or at least the cost is spread through-out processing.