It seems legit.
This week’s comic is likely more amusing to me and a small handful who rode with the same trainer I did as a teen (you know, back when I was still deluding myself that I was brave enough to be an eventer).
During one glorious group lesson– where ponies were dumping kids into the shrubbery right and left– my sister’s pony decided he was done for the day and started sucking back ever so casually before ducking a shoulder and sliding into the base of whatever he was pointed at.
In what I can only assume was a moment of frustration, our trainer at the time yelled as they approached the next fence (and said rotten beast started his reining horse impression) “Kill him!” And then, when he subsequently still slammed on the brakes after much kicking of small legs, “KILL HIM HARDER!” Apparently our trainer must have found my sister’s murderous effort to be lacking.
In any event, this glorious phrase, naturally, became the go-to any time a quadruped started snarking.