I don't see how we know enough about the relative timelines of different aspects of the rebellion to make a blanket statement like that. Provided there's roughly nine months between Ned's wedding and Jon's birth, which isn't ruled out by any solid evidence that I'm aware of, there's time for Ned to have slept with some woman, somewhere.The timeline doesn't work out for Ned's slippage, which is one of the major pieces of evidence there.
I don't think it's "heavy-handed" either, but I do think the hints in that direction are abnormally heavy for something that is, by the nature of the genre, going to be a long-term mystery, and the theory is more common among devoted fans than any other. Again, contrast some of the major resolutions we've already seen, which were amply foreshadowed without being widely guessed at. Then again, maybe GRRM's occasional frustration at the heavy fan discussion of this topic is because we've figured out something he thought was cleverly hidden.I have found a great many people who never caught on to the hints of the RxL=J theory, so I don't think it is really that heavy-handed.
Anything's possible, but I think it would be far truer to the character's emerging nature for him to remain with the Watch, regardless of how its mission changes as the series progresses. The need for a border force wouldn't necessarily end with the fall of the Wall or the defeat of the Others. And the oath is for life, without any contingencies. I don't really see GRRM writing an ending so rosy that there's no longer a need for the Watch, but you never know.Also, Jon's oaths may come to an end if they defeat the others or the wall falls, or any number of other reasons. I don't think he will forswear, but I don't think he will die on the wall as an old man either.
Given the complexity of character and moral ambiguity that characterize the series, I don't think it's at all a stretch to imagine Ned, caught up in a rebellion that could end his life and ruin his family, and only recently married to a woman for whom he had no reason to feel affection, straying from his vows. My complaint about this scenario is that it seems too simple-- there has to be more to it than that, another layer of intrigue or surprise. Really, that's my complaint about all the theories of Jon's parentage so far: none of them have quite the edge that I associate with GRRM's plotting.There is no way in hell that Jon is Ned's kid if solely for the fact that it is rather out of character for Ned to have an affair of any sort even if he had only seen the wife a few times.
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