Re-watching Jurassic Bark, look who's third eye I spotted in the trash as Fry throws the pizza onto the desk before being frozen.

No, it was always in the original. David X. Cohen states this specifically in the commentary to "The Why of Fry." He says that he was eager to write that episode (The Why of Fry) because it was “one of those ones that we were thinking about doing all the way back from the beginning when Matt and I were checking out the show, before there was a staff, a cast, animators, anything. The idea that there was a bigger conspiracy behind why Fry was in the future. And in retrospect, I wish maybe we had done it in an earlier season…” So the shadow was always there in episode 1 and the idea that Fry had been pushed was planned from the start. They just took their time about developing that idea.

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