Sorry for bumping this but pretty sure it is just a bit as Rin has already met Eiji's mum when they both got caught in the rain (chapter 48 to 50) and when they became official (Chapter 82).Well, from the looks, sometime during college, Rin had to put her relationship and fluff apart to focus on acting and modeling jobs until Eiji landed a job at the same TV station Rin was as an actress.
So yeah, looks like they put a hold on their relationship for few years a bit after starting college since Rin even state that she never met his parents.
But what if Rin got a better deal at some other TV Station? Or even Eiji himself got something better for his career? I thought the whole point of the end was they would work things together, not to each of their own until the world give them another opportunity.
This and the heavy drama at the end put a sour note for this great manga.
I think what rin meant was to inform their parents about them getting engaged.