I can confirm the offer as I've just signed up for it
I was on the Base Pack (£11 per month) and signed up for the Family Pack (£19.50 ) and now I get Sky Sports 1, 2, and 3. Had I just added Sport to my Base Pack I'd be paying £31 per month but this way I get more channels and saving nearly £12.
If this works then it's a win/win offer