Your assumption is incorrect as there are factors other than the processor in determining whether or not a given Mac can run in 64 bit mode. There are at least three things that must be present to run full 64 bit mode:
  1. A 64 bit capable processor such as the Intel Core 2 Duo
  2. A 64 bit Extensible Firmware Interface (EFI). [Wikipedia - EFI is a specification that defines a software interface between an operating system and platform firmware. EFI is a much larger, more complex, OS-like replacement of the older BIOS firmware interface present in all IBM PC-compatible personal computers]
  3. An operating system such as OS X 10.6.x (Snow Leopard) that has a 64 bit kernel. [Wikipedia - the kernel is the central component of most computer operating systems. Its responsibilities include managing the system's resources (the communication between hardware and software components).]
NOTE: Apple disabled 64 bit kernel support for any MacBook computer, even those with a 64 bit EFI.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein