The difference in this, is you would be using a 3rd party device. What if you use the cable companies DVR? It would not have access after dropping the cable company.
My point was that it isn't illegal like people were suggesting. If it is illegal to allow customers to continue watching their recordings after the cancel service TiVo and Microsoft have been openly breaking the law for years. Even if that weren't the case what reason would the government have for making a law like that?
For whatever reason TV providers don't allow you to keep accessing your recordings when you cancel but third parties do. This could be due to several things. When you cancel Dish they have no incentive to allow you to continue using their equipment. The could be doing this as a retention tool. Many people stay with a provider simply because they have a DVR full of content they haven't watched yet. For those people Dish would be helping them make the decision to leave if they allowed them to continue watching their recordings. TV providers have reasons to block this while 3rd party equipment makers could care less whether you have an active cable subscription or not.