No it isn't, you should read The Selfish Gene by Dawkins. There's a chapter explaining that this is a myth with little grounds in reality.

There's a lot of backstabbing and competition that goes on within individual hives of the social insects.

I've read it, a long time ago. IIRC, there is competition among the very few breeders, but the non-breeding workers are in fact identical. The social cohesion parent was talking about happens among the workers.