(Spoilers Extended) How did fans ever fall for this?

The more I think about it, the more I realize that Ned warning Cersei that he knew the truth isn't what got Robert killed. Why do I say this? Because by the time that conversation took place, Robert was already miles away from the capital, on the boar hunt and probably already drinking the fortified wine.

That makes me wonder why fans ever got this mixed up in the first place. Like..........where did people get the idea that Cersei came up with her "plan (if you could even call it that) to have Robert killed after Ned warned her? Robert and co. were days away from the capital. If she came up with the plan to get Robert drunk only after her and Ned's conversation, then that would've required her to have to send a raven to Lancel, and there's no way that he would've been able to read said letter before Robert himself, Renly or Ser Barristan.

Then there's the fact that when Cersei and Tyrion spoke about the coup, she told him that if Sansa hadn't told her about Ned's plans to get her and her sister out of King's Landing, she would never have known that she'd have to make plans to have Robert killed.

There's also the fact that when Ned confronted her, she didn't even try to deny it, she openly and proudly admitted her incest. That should be an implication that her plan to have Robert killed was already set into motion long before they had their talk.

Long story short, whether or not Ned decided to warn her wouldn't have changed a thing because Robert still would've died on the hunting trip.