I agree with the OP, Garrosh never betrayed Cairne. It was Cairne's own actions along with the betrayal by Magatha that got Cairne killed.
It's just that Blizzard is desperate to get everyone on the Garrosh-hating bandwagon and they're running out of options to throw at us.
It's silly when you think about it, because it's not that hard to get everyone to hate Garrosh. They just should've let Garrosh applaud the Stonetalon incident instead of executing his subject for it and showing honour. They shouldn't have put Garrosh in the grey zone, instead they should've kept his hard line from WotLK up until MoP, that's where they failed and now they're making up excuses about betrayal to make up their earlier mistakes to guide the storyline in the direction they want it to go.