AES mode which verifies data integrity AFTER decryption
Yes, you are correct, as long as it really only is the AES part which could dysfunction.

Quoting another source, for example Wikipedia's CCM page:


  These two primitives are applied in an "authenticate-then-encrypt"
  manner, that is, CBC-MAC is first computed on the message to obtain a
  tag t; the message and the tag are then encrypted using counter mode.


Note that we generally do not recommend to do "Mac then Encrypt", however CCM is a mode of encryption which features its very own proof of security, so you are good to go.