When on multyplayer and invisible both the armour and tool movements are liked to the nearest player to the invisible one.

To recreate do this: Get two people then one of them needs to drink an invisible potion. Then the person needs to ether wear helmet (pumpkins work the best) or hold a sword. Then the person that invisible needs to stand still (and be in f5 mode) while the other person needs to run and jump around.

If you recreate it you will see that the "bobbing feacher" where the sway of both the head and held tools move the same as the non invisoble player.