Perfect trees will only grow from perfect fruit in the town that they are native. If you give someone a bunch of perfect fruit from your town and they don't have that fruit natively, planting them will yield regular trees.
To get anything else to yield a perfect tree, you need to use Fertilizer on a sapling, but this hasn't been tested with non-native fruit anywhere I've seen.
In short, if the perfect fruit is a fruit native to the town, planting it will always grow a perfect tree. The game does not (and cannot) differentiate between a bunch of fruit. Otherwise you couldn't stack them. Anything that is unique to you (such as a signature sheet) isn't something you can drop, anyway.