What you said DOES make sense.
However, I interpreted Rae´s reluctance in admitting that she and the MC are a "couple" or "lovers" differently. I mean, by the time you get the pool, it is quite clear that Rae has either fallen for the MC, or is about to.
You see, we know that Rae is 1- part of a Infernal Noble House, and 2- Her duties in that House are related to diplomacy and espionage: in other words, pursuing the House´s interests cleanly if possible, but if it is not (or maybe simpler/more expedient), then is cloak and dagger time.
We don´t know what Rae and Lady Sire said to each other in their conversation (last part of Rae's story so far), but considering that he MC seems to be RIDICULOUSLY powerful (and in: he is an anomaly that shouldn´t even be possible) in Ether-related magic, it is quite possible that Lady Sirena decreed that the MC is/could be an asset to her House, and ordered Rae to either A- secure said asset´s loyalty for her House, or B- failing that, dispose of it before any of the House's enemies can grab it.
IF this hypothesis is correct, then that would explain Rae´s reluctance, for she could receive orders at any given moment, and those orders could end the end of her relationship with the MC, so it better not to get too emotionally involved.
Which, if we think about it, kinda sets up Rae's story: How willl she deal with her old loyalties and her new life's perspective? What will she be choosing, in the end? And how the MC is going to deal with that?