"It's not at all inexplicable. The first few iterations of Core 2 Duo machines ran 32-bit kernels. More information here:
Mac OS X v10.6: Macs that use the 64-bit kernel
This box uses a 32-bit kernel that supports 64-bit applications. It has a 32-bit EFI, so its days are numbered with Lion. There are no updates forthcoming with this system. Shame, that, as 6 GB RAM and a 960 GB SSD ensure that it's still quite spritely despite its declining years.
I'd complain about the tethering, but I've never actually even tried to do USB tethering. So I'll hold my whining for another day."
I knew I should have qualified that "inexplicable" 🙂
Yes, I'm aware that the first Core 2 Duos (and other machines) ran 32-bit kernels.
What is "inexplicable" to me is why anyone with a 64-bit capable machine would still run a 32-bit kernel these days, given the existence of easy apps like "32- or 64-bit Kernel Startup Mode Selector", plus the fact that it lets you address all your 6 GB of RAM address space instead of 4 GB per-process.
I'm aware that someone with a 2 or 4 GB system might say "Why bother?", but to me the compelling argument is that the slight performance hit is worth it given the fact that Apple is throwing 32-bit users under the bus - either by design or by accident.
(Conveniently "forgetting" to put a dual-architecture .kext into the iTunes 11.4 distribution is another signpost on that road. The fact that they wouldn't release an updated bash and sh for 10.6.8 to cure the recent "Shellshock" UNIX® shell vulnerability is another case of throwing the users under the bus, too.)