I stayed on rented points at AKV back in October. We became members in September and I had my
DVC member card when I checked in. I explained to the CM that the reservation was rented since we weren't members when it was made. She told me that I was absolutely entitled to free internet. (I am not trying to contradict the policy, I'm just restating what this particular CM told me) When I received my express check out invoice, I saw that I had been charged. Since I did not know the official policy at that time and the check in CM assured me that it was free, I went to the desk. I politely showed them my member ID card and pointed out that I had been charged for the internet access. I also re-stated that this was not my own reservation but a rental and if I was not entitled to the free access, I would pay for it. This CM also told me that it is free for members. Again, I am not trying to argue what the policy is or is not. I am just relaying my own experience.
As Brian pointed out, your experience may vary. It never hurts to ask.
On a side note, I am a little confused as to who gets free internet and how they determined it.
FREE: Members staying on THEIR points; Members staying on TRANSFERRED points; GUESTS (not renters) of members booked on points
NOT FREE: Renters, Members staying on RENTED points, any guest staying on cash
So, what confuses me is why members staying on rented points are treated differently than members staying on transferred points.

I would think that if you are a member and staying on points, it should not matter where those points came from, right? I must be missing something. Wouldn't it just be easier to say that any DVC member staying at a DVC resort is entitled to free internet? Points, cash, my points, your points, Mickey's points...what is the difference and why does it matter? I am

.