Nobody has said this yet, but I thought it was so obvious. Egwene did not personally "reject" Rand's offer (whatever his offer was). In fact, the likeliest scenario is that the rebel AS didn't know what to do with Rand's emissary because Egwene had just been captured by the tower AS. Think about it. The rebels don't want to appear weak and they know that if the Dragon Reborn acknowledges Elaida as the Amyrlin that their rebellion is almost certainly doomed.

So when Rand's emissary arrives, Egwene is already gone and the remaining sitters (either Romanda or Lelaine most likely) is the one who "rejected" Rand's offer. Rand blames Egwene, but she didn't make the decision most likely. Probably the rebel AS are trying to keep it secret that Egwene has been captured and they probably wanted to keep it secret from Rand's emissary too. Rand's emissary probably was requesting an audience with Egwene, but when he was denied the audience he probably got angry which only added to the already volatile situation. I can easily see how Rand's offer got rejected in these circumstances.