I may indeed stand corrected. From the lodestone:
Gathering: Reduces the depletion rate of the Remainder gauge.
Perception: Increases a player's chance to find higher-quality items.
Output:
Increases the amount of times a miner or botanist can gather at a single point, as well as reduces the amount of time a fisher must wait for a bite.
So I suppose it depends on your definition of quality. I had assumed quality = rarity, which now you mention it may not be the best interpretation compared to +1/2/3.

That being said, sacrificing perception for gathering and output can only assist your overall SP haul.