kernel modules: must be compiled against kernel image?
 

Do kernel modules have to be compiled against the exact kernel image it will run with?

For all intents and purposes, Yes.. 99.99% of the time, the modules should be (re)built too if you are making a kernel, and they should be made from the same .config that is being used to make the kernel..
Is there a specific circumstance you are wondering about?

not really, I was having an argument about it with a friend.

:p and who won?

me :D .