Ngl, Rei throwing Rio under the bus too and causing her to freak out was absolutely delectable and probably the only action of his I can appreciate as a reader. Cheaters tearing each other apart as their web of lies crumbles will never not be satisfying.
This also really makes it obvious that, to Rei, the whole affair was just about fooling around, not love. If he actually did this because he loved and wanted to elope with Rio he would be defending her and their relationship.
What Rei actually wanted was a slave at home to do all the house work for him and keep his mommy satisfied and a side piece to have sex with with no strings attached. Rio was as disposable and irrelevant as Mahoro to him, and she learned it the hard, but deserved, way.
So Rio went on this huge ego trip to make Mahoro's life miserable over a man who only saw her as nothing more than a sex doll. How's that for poetic justice.