The only measure by which I believe it would be acceptable to judge Linux "fat" would be to compare the size of kernels generated using "tinyconfig". Basically, everything that can be disabled without rendering the kernel useless it turned off. You're only left with the core of the kernel. At this point in time, you get a kernel image that's like ~450 KiB.

If you actually want to boot that on real hardware, you can enable the drivers that are stubs into the BIOS calls for classic devices (disks, serial ports, SVGA graphics, etc.) for another ~100 KiB. It's extremely limited though - no specific PCIe support, ACPI, networking, etc.