I can understand your frustration. I have the same sentiments about the reason for refusal, it does not make sense at all.
I talked to a lawyer and he advised me to get a copy of the immigration officer's complete notes on the case. This way, we can identify the real reasons of refusal so we can better position ourselves to reapply.
It takes 30 days to get this.
Unfortunately for me, my LMIA has expired so we are not in hurry to get it.
You cannot appeal the decision. You can only file a judicial review application if you feel that the application was improperly refused. You need a lawyer for this, and it does not guarantee an approval. The judge may decide that there was no error in the refusal process or may decide that another officer must re-evaulate the application.
Goodluck to you.