When running /execute on owner as an arrow, commands are not run as the owner, despite the arrow having an Owner in its NBT.

Steps to reproduce:

fire an arrow from a bow or crossbow

/data get entity @e[type=arrow,limit=1,sort=nearest] Owner

(confirms that arrow has an owner)

/execute as @e[type=arrow,limit=1,sort=nearest] on owner run say hello world

Expected Result:
Arrow owner says "hello world" in the chat

Actual Result:
Nothing is said in chat

Why it is expected to work:

taming a wolf then running the same commands but replacing 'type=arrow' with 'type=wolf' on the tamed wolf works. Both have the same Owner NBT tag in the same format, thus they should function the same way.