You know, my pigs won't touch it. I even went out and purchased the organic rabbit ones. I left them in the cage for over a month and they took one nibble and that's it. I tried different sizes etc..
Of course, my boys have a large cage with lots too do, and they also have those alphabet blocks. They LOVE their alphabet blocks. One of them will even sit there and look at the little picture on the block, pick it up, turn it over, and look at it again. What a cutie! They also have wooden hidey homes and those straw nest style hidey's along with that they have a cardboard box unlimited timothy hay. They will nibble on the doors of all those things on occasion.
I have no idea if all that has anything to do with their lack of interest in apple sticks.
I recently saw a post where someone said most pigs never touch them either.
As far as using from your own tree, I think the only thing to worry about are any kind of pesticides, herbicides or fungicides that the tree may have been sprayed with.
I wonder if they don't like the bark, but like the white part?