This is not accurate. I was able to get the
Easter Egg Exploit to work just fine on a 5659 dash (upgraded by the game Ninja Gaiden, I do believe) on an older Xbox (kernel 5101). So long as the kernel is earlier than 5713, EEE seems to be the safest hack to install (a bad signature or some such installation problem will still let you boot normally to the dashboard). If the kernel is 5713 or newer, don't even bother looking at UDE, look only at UDE2.
At this point it seems your question does not have to do with GameSave Exploits. Check out the pinned posts in the XBE Hacks forum for details on these exploits.