I think you were on the right track in your first post. The context of the LOC quote (which has been discussed a lot before in this context, by the way) is very important, because Semirhage was precisely expressing her worries about the DO's "whims", all the secret moves he made on the board, the introduction of a new player like SH, and she feared all along the DO might expend even pieces as powerful as his Chosen to achieve a specific goal.

Also important was the fact she mentions in that scene that she would kneel even to al'Thor if the DO made him Nae'blis...

So that's definitely foreshadowing. In the end, Shai'tan chose to gain power over Rand over Semirhage's life.

This scene is also completed in TGS with the Moridin/Rand conversation that set the stage for the betrayal of Semirhage. Moridin confirms Semirhage's greatest fears: the Chosen are fools whom the DO intend to betray in the end as there will be no reward but the end of Creation. Moridin also gave Rand the means by which he could prevent transmigration. Moridin cannot betray Shai'tan, because he is addicted to the TP and Shai'tan is also the only way Moridin can get what he wants, so.... what he told Rand wouldn't have displeased Shai'tan. Moridin/Shai'tan thought they had Rand pretty much in the state where he'd wish to end it all.

Also, there's the fact Jordan has long ago answered straight out how someone can use the TP, seeking to correct misconceptions about a pre-established connection and stuff like this (he must have known even then Rand would be given access down the line). There's three conditions for a human: the ability to channel, knowing how to embrace the TP (that is what Rand seems to have gained from Moridin, inconsciously), and Shai'tan letting you. It isn't and never was a question of connection to Shai'tan (the whole theory about Rand using his mental link to Moridin seems very much like a new variation on these misconceptions that you need any special connection....). It's very unlikely there's more to it than that. When there was aspects he chose to keep secret, Jordan had the habit of adding "there's more than that... but RAFO", as he did for several similar topics, like transmigration, the making of Grey Men, how the Chosen picked their powerbases, or even the purpose of the Dark Prophecy etc. For the TP access, he gave repeatedly a straight out answer with no caveat (and that's reflected by everything the Chosen have said about the TP in the series). It's fairly obvious RJ intended us to interpret what happened in TGS as the DO havinggiven Rand access to the TP. How everything went downhill with Rand right after that (even his ta'veren nature seemed affected - nothing the Wheel had been pulling him toward lately worked.. failure with Tuon, with Cadsuane, in AD, with the Bordermen, hitting a wall with Nynaeve about Lan... and in the end almost destroying the world...) sort of makes it obvious why the DO chose to betray Semirhage when she made the big mistake of torturing Rand, putting him in the state where he could embrace the TP (that's when Shai'tan took the decision, IMO. I don't believe it was all along a set up. He meant Semirhage to capture Rand, period. He betrayed her when she open an unexpected opportunity to bait Rand to use the TP)

Brandon is just walking on eggs with these answers, because AMOL is the last book and forcibly has many answers, but it's been split in three. Brandon is quite a bit in the position of giving us answers about the book when only 1/3 of it has been read, and forcibly issues set up in acts 1-2 will stay around for act 3 as well. It's no wonder he's trying to avoid confirming much of anything, and that he's being vague. In this specific instance, the fact he pointed out to Semirhage and her reaction is pretty telling, though (he brought her belief up, not the persons asking the questions who didn't even mention her)