In the books, sure. I don't think the show is interested in doing foreshadowing and character-motivation logic on that level. All that matters on TV is that Joffrey has a general motive (he hates Tyrion) and opportunity (Moore was a Kingsguard, sworn to follow the king's orders). I mean, technically Joffrey (who doesn't believe the rumors about his parentage) has less reason to order the bastards murdered than Cersei (who knows the rumors are true), but the show explicitly assigned that to him as well.
Oh, and Robert was given unusually potent wine, not wine that was poisoned.