Distinct MAC and Key for AEAD? I am implementing some of the algorithms in RFC 7518 and I noticed that AES_CBC_HMAC_SHA2 contains the following paragraph:


  
  The secondary keys MAC_KEY and ENC_KEY are generated from the
     input key K as follows.  Each of these two keys is an octet
     string.

  MAC_KEY consists of the initial MAC_KEY_LEN octets of K, in order.
  ENC_KEY consists of the final ENC_KEY_LEN octets of K, in order.

  
  The number of octets in the input key K MUST be the sum of
     MAC_KEY_LEN and ENC_KEY_LEN.  The values of these parameters are
     specified by the Authenticated Encryption algorithms in Sections
     5.2.3 through 5.2.5.  Note that the MAC key comes before the
     encryption key in the input key K; this is in the opposite order
     of the algorithm names in the identifier "AES_CBC_HMAC_SHA2".
  


Why would the encryption key be different than the MAC key? The examples I see in wikipedia show that the same key is used for both. 

My understanding is that because in JWE only the message is authenticated, it means that the key is available for tempering and since the MAC key and the MAC are in a known location, it should be possible to forge messages.

Am I incorrect in that assumption? Why did the RFC authors chose to split the keys instead of reusing it?
The examples I see in wikipedia show that the same key is used for
  both.


Doing so is fine in most constructions, however "most" is not "all". Also the graphics could be read as "derive a key from the given input key somehow".


  Why would the encryption key be different than the MAC key?


Cryptographically speaking, it's cleaner to use different keys for the different primitives, as it definitely prevents subtle interactions due to the key-reuse and thus makes formal proofs about security claims easier. 

Also there are cases where you actually have to use different keys for the MAC and the encryption scheme, the most well-known example being the combination of CBC and CBC-MAC which allows for modification of (nearly) the whole message on key-reuse.