Do summoned pets get stunned?

[Videri]

I am not sure all mage pet nukes and roots have cast times. I think the fire pet casts a nuke (cast time), but I'm pretty sure the other innate abilities are all procs: earth pet root, water pet small nuke, and air pet stun. I could be wrong. I think we would want to confirm exactly which of their abilities have a cast time before surmising that summoned pets cannot be stunned.