I can tell you definitively - You are 100% correct. On the PS3 I downloaded/deleted/redownloaded games repeatedly.
On a side note - this is why I download EVERY free game you get on PSN each month. Even if it's not your cup of tea - once it's in your library you can delete it and come back to it if you have a change of heart. You may never come back to the game - but at least it's in your library so the
option is there.