Amelia,
I am not aware of the Watchtower's explanation you are referring to. However, from Galatians (which was genuinely written/dictated by Paul) he gives accounts of his experiences that are completely at odds with accounts in the Book of Acts (written some 30 to 60 years after Paul's death).
For instance, Paul says his visits to the leaders in Jerusalem were very private affairs and that the people only knew him by reputation, not personally. Acts 15, however, creates a general conference in which Paul addresses the whole assembly. Also, Paul was returning to Damascus, not going there.
The Book of Acts is a contrived religious fiction created for a local purpose at the end of the first century. It is evenly balanced between accounts of Peter (first half) and accounts of Paul (second half). One theory is that this was done to counter the positions held by Marcion.
Doug