In my opinion targeting by the site the user signed up on isn't much indication on push traffic, Since the user could have signed up at a file sharing site for instance and you got the user when he is on day 7 since he registred, do you remember on what site you were on a week ago? I think you should look at push on 2 params: Fresh and old and go from there.
In general I completely agree with that, it certainly isn't the defining parameter at all. The reason why I mentioned sign up date is that specific types of offers convert much better on users who have been signed up to Push Ads for longer, as newer users may be more cautious and hesitant to convert due to less trust initially (well that was the strong correlation when I used to run offers through Push)