"I don't honestly know why they offered me the part in Rent"

Adam Rickitt's quote is likely describing his experience of being used a part in the musical Rent. It is possible that he is revealing his surprise and confusion at being offered the part, as he does not know why he was selected for the role. It might be that he was chosen since of his talent and experience, or since the casting directors saw something unique in him. It could likewise be that he was chosen because of his fame and popularity, as he was a well-known actor at the time. Whatever the factor, it is clear that Adam Rickitt was shocked and humbled to be provided the part in Rent. He likely felt honored to be chosen for the function, and was grateful for the chance to be part of such a renowned musical.