I saw it more as Perrin standing up for Egwene after what they had been through together with the Tinkers & whitecloaks. I didn't really read it as 'Romantic interest'
I think it's kinda dumb too but I also come from a perspective that Moiraine is probably acting on disinformation to a degree. She didn't even know the Dragon was Rand until he told her, just that it was 'one of them'. Moiraine isn't all knowing in this incarnation it seems to me.