The literal end of that entire paragraph, and update as a whole, was that he could not lie to himself that he did not see Viserys as a legitimate Sovereign in his own right, as opposed to a criminal/mad dog that needed to be put down. He couldn't basically make us his Straw Targaryen, essentially, unlike Robert.
But even with that, even acknowledging we had some legitimate right to rule (somewhere, not necessarily Westeros, though the former is a dangerous, dangerous stance to take considering who we are), he still said he would support Robert.
And, months later, without us having any idea of what's going on in his head, he starts doing things that make it look like he's drawing closer to our faction.
@egoo If you want my honest opinion, rather than delegating an action to a bunch of characters who will awkwardly play the "you know what I'm doing here but you can't acknowledge it outright because it would absolutely be treasonous to do so" game, maybe we should just finally approach Ned Stark and get him onsides. Casually mentioning we just rescued five thousand Thenns from an army of wraiths and one of our Companions slew an Other champion, and then go "oh and by the way, have I mentioned that I'm rightful ruler of Westeros lately?"
Rip off that band-aid finally.
Edit: On the other hand... that could take time, and it would also likely result in the North becoming intensely interested in Southron politics if we failed. Which could be a bad thing. Mostly for the Starks, of course, but also because it would be distracting for us.