Sorry, you are wrong, yes it can. As long as I don't cancel it and it stays active on my account, when it's sold, I call TiVo and they assign a case number which allows service transfer for the new owner. The new owner must take that case number and call TiVo to activate it on their account.
It's exactly the same as lifetime service transfers, New owner assumes the orginal service contract, be it lifetime or cheaper monthly rates. It's not common with selling monthly service TiVos as used TiVos are taken out of service and such typically doesn't apply. This is the key as service can't be interrupted by the discounted rate owner, if so then the normal higher rates apply.
I guarantee the buyer will receive the lower rate and if not pleased, I will refund the purchase amount. In fact this orginal TiVo that had issues was one I sold to a member here, he had a problem with the cable card so he returned it to me and I refunded him his money. After receiving it back, it was replaced by TiVo under warranty and this is the replaced TiVo.