I don't think it's a good idea to plant any tree near a fence. The problem is that as it grows, it may end up actually hitting the fence, possibly causing damage to it.

Also, you end up with part of the tree on the other side of the fence, so it's difficult to take care of it. And if you're planting fruit trees, your neighbor may not like the mess when it starts dropping fruit in the lawn (although the ability to pick fruit without needing to pay for the tree may mitigate that).