This perspective doesn't take into account how much influence posts older than 7 days have on one's likelyhood of voting on a poster's newer content though.
For example, I first read Jerry's work in a crazy old post on a topic I did a search for, and immediately upvoted newer content of his that I found interesting, directly afterwards.
So the first post did have a payout long after a week had passed, just indirectly...
Yes - that's true!