What I expected to happen was...:
Summon a Vex with no items in his right hand

What actually happened was...:
It has an Iron Sword in his right hand.

Commands to Reproduce:

/summon Vex ~ ~ ~ {HandItems:[{id:air,Count:1},{}]}

/summon Vex ~ ~ ~ {HandItems:[{},{}]}

(If you say it's specification. I want change this specification.)

As of 1.11-pre release 1, spawn eggs are still unable to do this, however, this is a client side glitch and reloading the vex fixes it (as server side it has an empty hand)

/give @p minecraft:spawn_egg 1 0 {EntityTag:{id:"minecraft:vex",HandItems:[{id:air,Count:1b},{id:air,Count:1b}]}}