If one were to say that the day of the week on which it rained was Tuesday and no other day, one would say "It rained only on Tuesday".
One could argue that "It only rained on Tuesday" would also be acceptable. However it could be argued that "It only rained on Tuesday" implies that the only thing it did on Tuesday was rain. While the first way is definitely clearer, could it be argued that the second way is also correct, albeit open to misinterpretation?