Yes I do mean boosting up to 1000.
I have never, ever seen a tree boost to 1000 without an event; and I've run the game for hours on end with a program monitoring changes in memory-addresses to log changes in the number of fruit on a tree. (In fact, I let an entire starting village die in order to get the numbers, since they would assuredly harvest no fruit. I propose a toast to their noble sacrifice.) They gain 111 fruit each every three hours. Anything else is due to an event, such as the fertilizer event. (A villager finds some beans - one option is to grind them for fertilizer)
I don't train any of my villagers to be JUST farmers.
Irrelevant.
Even without being checked for farming, if they have the skill they will still strip trees - perhaps not as zealously, though..
If they have farming skill, they will farm. The only way to prevent them from farming is to let all your farmers die without training more, or to pause your game every time you walk away from the keyboard or close the game.