We can safely assume that the father and sister had the same surname. If the billing address is the same, then it adds as further evidence that the account isnt being traded away.
What you have posted is an exceptional circumstance. In your example, what Blizzard wanted was proof that the account wasn't leaving the family. Name is obviously going to be the first port of call. Given the circumstances you've mentioned, Blizzard obviously AGREED to the account split, and asked that the billing address remain the same as further proof that the account wasn't leaving the family.
So he wasn't VERY wrong was he? He wasn't wrong at all.
Your post makes perfect sense and in general I agree.
What if the sister was married and had a house of her own? Like you said though, different circumstances. You are assuming quite a bit yourself and about Blizzards inside policy.