if someone says that they are reviewing the "kernel proper", what are they talking about? the source code?

Never heard that one before, but I would have to venture a guess they were talking about the kernel itself, not the source code. That's just a W.A.G. on my part though...

what they probably mean is the kernel raw as presented at kernel.org
as opposed to the many hacked and patched / altered versions distributed in binary distributions.

I interpret the phrase simply to mean, "the kernel, as opposed to the many other layers of software that are wrapped around it."

"The kernel" of an operating-system is the central "system control program" that actually operates the hardware of the machine. The kernel is loaded into memory at boot-time, and it stays there. (In Linux, the kernel also includes loadable kernel modules, which function as part of the kernel when loaded.)

Most programs never deal directly with the kernel: they use shared libraries such as glibc to do nearly everything.

yes yes that makes perfect sense "from within the kernel proper"