Closest distance between a villager house and a rock?

They can be 1 'tile' away. If you're not sure on this, I can take a screenshot of one of my villager's houses being one tile away from a rock.

Rule of thumb with empty space for building placement is that is can be 1 block/tile away from the river, lakes and rocks and two tiles away from buildings, villager houses (player house included) and I believe three tiles away from the town plaza. Not sure on the town plaza, though. That one's just from personal experiences.
 
My villager robin moved (by default she was a starter) by a rock with a one space gap.
 
To me it always seemed animal villager houses took priority over everything else. There were plenty of times I'd try to add a pwp somewhere that wasn't remotely near anything and Isabelle would give me some annoying bs answer. Low and behold, later on someone plotted exactly where I wanted a much smaller pwp. It's stupid.
 
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