I'm not sure that the episode with the dead dog opening quote _is_ the episode with the dead dog (a spoiler), maybe was a previous one and because it was somewhat controversial this is a joke about it.

Can anyone confirm?

The two possible jokes works but are different, for me a pun of a previous episode is so much funny.

I mean to say - I won't watch the episode with the dead dog. So they fact they recognize that and added as meta info later was interesting.

It seems that it's from "Stench and Stenchibility", from the last season of the show... so, much later than "Jurassic Bark".

Thanks! It's a great meta-joke then.