I played around with this a bit more, and I think the rule behind that behavior is something like this:
If "Emphasize Production = Yes" is set, then the governor will pick the forest, if afterwards the town has still at least +3 food. Otherwise he will pick the highest food tile.
Boohh!!! I already uploaded pictures of Tenochtitlan and Teotihuacan that contradict this. Okay, Spoonwood observed correctly that in my pictures Teno was a town upon growth, and Teo was newly founded, and this may be of influence, but here is Teno when it was newly founded, and already here the governor went with +3 food for this town...
..while in the case of Teotihuacan the governor continued picking the forest, also upon growth:
(until growth I had let Teotihuacan use the grassland tile, overruling the governor, as the forest tile just lost me food, while the extra shield got corrupted away - at least until the road was in place).
I've also taken Lanzelot's Karakorum save, and can show that the governor picks different tiles sometimes, depending on what's already being worked. This is the same town a bit later. Karakorum is about to grow again, and the worker is about to finish a road on the river-forest tile:
This is after growth:
The governor has picked the river-forest tile, accepting going back to +2 food.
My hunch is that it's the commerce that makes him pick the forest tile over the grassland tile here. To back this idea up we can go back a turn and swap forests.
Here's Karakorum before growth again, but now it's already working the commerce-rich forest tile, and the only other forest available gives no commerce at all:
Here's after growth:
The governor has shunned that commerce-poor forest, and picked the river-grassland instead.
Still this is by far not enough evidence to make any firm conclusions, but it seems that the governor doesn't have any strong preference between +2 or +3 food and that other factors come into play then.