I don't really know what happened, and no other leash bug seems to be this bug.
I decided to spawn an iron golem using /summon (I put {invincible:1} to try to make it invincible. I used an NBT editor to make it invulnerable).
I then tried to tie it to a nether brick fence (which already had snow golem attached to it, which have their own issues) and the lead got attached to the block ABOVE the fence. I don't know how this happened...
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What? How do you explain the TWO SNOW GOLEMS I have leashed to the fence below that one?
In any case, no matter the reason, this is a BUG.
I spawned (this time with the right tags so I didn't NBT edit externally) another Iron Golen and attached it to the same air block.
I think this may duplicate issues I missed while searching...

Duplicate of MC-14680
That's because there is already a leash on the fence, and fences only accept 1 leash at a time.