Re:Yes it does! (Score 1)

please give a non-contrived example where you can do something like overwrite the EIP with an arbitrary value and still not be able to execute arbitrary code

If writable memory pages aren't executable (W^X, NDX, I don't recall the acronyms), your program can't execute runtime-supplied code, evah. Either setting EIP maliciously or not, you won't be able to "jump off and execute" any code which was not present at the time of compilation.

Were you trying to prove a negative proposition? Pretty basic mistaek, dude.