When "your nose is out of joint" you feel upset, because someone didn't treat you right.
As to your original question:
"You can't smell a rat when your nose is out."
"Smell a rat" is an idiom meaning that someone is suspicious of something.
When your nose is out it doesn't work the way it should and you probably can't smell.
So if you can't smell, you can't smell a rat and therefore can't be suspicious.
Let's say we were undercover agents in some sort of criminal investigation, and let's also say that we were meeting up with our target, one big gangster boss. He would certainly want to check if we are who we said we were, maybe by running our names and faces against some database on the internet. However, you anticipated this and sabotaged his connection, and with a subtle smile on your face you whisper into my ear, "You can't smell a rat when your nose is out."
Sorry, I got a little carried away, but I guess you'll get the picture.
*not a teacher*