You sign your letter and seal it in an envelope. I put your envelope into a cardboard box and give it to your friend. Your friend refuses to open your letter because you did not sign my box.
No, this is more like your friend refusing to trust the contents of the letter after the mailman cut the letter into small pieces and glued them back together.
I think that would be more analogous to receiving a message, parsing it, then realising the payload is another signed message, and then validating that.
Depending on the situation, signing the container might not even be necessary, much like a zip file without a password that only contains encrypted contents anyway.