Also, let's not confuse Guard/Standby with Sic/Obey. Just because a pet is on Guard, does not mean they are on Sic.

Can be...

Guard/Sic = Will attack a target you attack or a target that attacks you, and will use all abilities
Guard/Obey = Will attack a target you attack or a target that attacks you, but will only use the basic attack
Standby/Sic = Will not attack a target you attack and will not attack a target that attacks you
Standby/Obey = Will not attack a target you attack and will not attack a target that attacks you

So even while in the video the pet is on Guard, it does not necessarily imply them being on Sic or Obey. In fact, there is no visual indication anywhere which mode they are in, except whether or not they use non-default abilities (Aerial Slash, Contagion) on their own.

If a pet ever uses Aerial Slash on their own, they had not previously been given the Obey order, or at least not since last summoned / instance started / were put on Sic.