" Are there any other items that I need to provide for proof so I can cover myself??"
Do you have curtains in the rental? If so, take one down and store it in a sealed plastic bag. These tend to hold smoke odors.
For what it's worth, my partner was a heavy tobacco abuser. When he passed away last July (from lung cancer; not a surprise considering his smoking history) I began washing the walls of the bedroom he used as a his workroom. Took pictures of a half washed wall; one side the original light blue; the other half a (literal) chocolate brown. The white blinds were also a dark tan as were the closet doors. One did not realize the extent of this until I began to do this.
Of course this was after 19 years of heavy smoking in this room.
Gail