Their C compiler is not reliant on having another C compiler around. Compiling the 16-bit real mode bootstrap for the Linux kernel on x86(-64) requires another C compiler; you certainly don't need another compiler to compile the kernel for another architecture, or to compile another piece of software not subject to the 32k constraint.

The compiler itself is entirely functional; it just can't generate code optimal enough to fit within the constraints for that very specific (tiny!) part of the system, so another compiler is required to do that step.