It's nothing to do with setOwningPlayer, it's a long sequence of bugs on both client and server.
Frankly stuff is so broken I'm surprised people haven't reported it before.
The only circumstance which I can actually see it working reliably is if you are 1) Running spigot, 2) Already have a tile entity with the correct skull, and 3) Use setOwner

I'm able to get your skull with that command in singleplayer and on the server, so I'm not sure what to add.

I cannot reproduce this.
I am not seeing any rate limiting in the client log either, but yet
/give @p minecraft:skull 1 3

Will not give me my skull.

Nor will setOwner(name) in the plugin.
It seems very touchy, but I am unable to reproduce anything which points to an issue specifically with setOwningPlayer.

My issue is not with the rate limit. I wait around 2 minutes between restarts, and am able to get my head using setOwner(name) every time. setOwningPlayer always gives me the alex head.

Reproduced in single player with
/give @p minecraft:skull 1 3

It also sometimes works in Spigot/CraftBukkit and sometimes doesn't.

It's Mojang's way too aggressive rate limiting on skins.
Wait some time and try again.

When I change it to setOwner(event.getPlayer().getName()), it updates to the right skin after a few seconds.

If you restart and rejoin too quick, you get rate limited and it won't work (as you'd expect).

I'm not seeing either method work in Spigot

Code:

@EventHandler
public void onPlayerJoin(PlayerJoinEvent event) {
    ItemStack skull = new ItemStack(Material.SKULL_ITEM, 1, (short) SkullType.PLAYER.ordinal());
    
    SkullMeta meta = (SkullMeta)skull.getItemMeta();
    meta.setOwningPlayer(event.getPlayer());
    skull.setItemMeta(meta);
    
    event.getPlayer().getInventory().addItem(skull);
}

Picture of my skin and the skull I was given.

Useful reproduction code please