Sir!! You are a genius  .

I initially figured out the mystery BTC address might come from doge's PK.


But obviously I am not smart enough to use the hexadecimal format of the PK, so I used the PK as is and it wasn't a valid PK for BTC so bitaddress.org used the Doge's PK as a passphrase to hash a whole new PK which obviously resulted in new different BTC address, but you nailed it, and hey thanks for sending me myBTC back. 



They can't recover the BTC sent to that addy, only you can do it, if you don't know how ask for help, and ingore any PMs from people who tell you they will help you recover your coins, any advice given must come from a trusted person on forum, the process is rather simple you can do it yourself, just follow what HCP did, if things are still unclear, ask here and members including myself will teach you how to do it.

After getting your money back, you should return the money they sent you, at least this is what I would do if I was in your place because no matter how you look it at, it's stealing!, you should inform them and if they decide that you should keep the money they sent for the inconvenience they caused you, then keep it, if they ask you to return it, please do.