Can a transcript change dependent random variables into independent variables?
Yes. Consider the following protocol.  Alice flips a coin, and sets $X$ and $Y$ to be equal to the outcome of the coin flip.  She then sends $X,Y$ to Bob.  Note that the transcript will include the value of $X,Y$.

Now unconditionally, $X,Y$ are dependent (there is probability $1/2$ that they are Heads,Heads and probability $1/2$ that they are Tails,Tails). But conditioned on the transcript, $X,Y$ are independent (e.g., if the transcript says they are Heads, then with conditional probability $1$ they are Heads,Heads and all other cases have conditional probability $0$; that meets the definition for independence).