Solving Recurrence: Repeated Substitution and Closed Forms

Although I have learned repeated substitutions before, I just recently learned that you can have another recurrence in your "closed form" as long as it's not a recursive function of the same variable. I never knew this until the third tutorial when the TA was solving a recurrence relation which kind of "contains" the fibonacci recurrence. I found this surprising at first because I always thought of a close form as "something I can plug in a given value of the variable and get the output".