A few points:
1) You're currently paying for DVR service, correct? Terminating your relationship with Dish means you're not longer paying for DVR service and that's what you want to continue to access. I think that was the point the poster you quoted was trying to make.
2) Because of the DMCA and DRM, there's no legal way for you to bypass the encryption and transfer your DVR content to another computer for playback or storage. There are supposedly Linux programs that will allow for this, but I believe discussing them would violate the no hack talk rule on this forum. The only way to keep things would be via analogue output to a DVD recorder or VCR.
3) As for your BluRay comment, I think a more accurate analogy would be that you wanted to rip the BluRays to a computer to then watch them on another device. Content owners don't would argue that this is illegal and that you should have to pay separately for digital rights to watch the content without the disk; that the license that comes with the disk is only to watch the content under certain limited conditions. Similarly, you may own the Receiver and the hard drive, but not necessarily the right to watched the licensed content on it outside of a service agreement with Dish. This may be Dish's doing or it could very well be spelled out in their contracts with the content owners. I don't think anyone here could say for certain. As for why Tivo is different, to my knowledge they have no contracts with content providers and thereby could be avoiding any such limitations. Since cable companies legally have to provide cablecards that are compatible with Tivos, I'm not sure there are necessarily even contracts there that could limit how Tivo treats the content after the underlying service is terminated.
These points aside, I think DVR recordings are a huge retention tools. I have several hard drives filled with content, and would be loathe to part with Dish and lose them. That said, if the service ever really pissed me off, I would either bite the bullet and forgo the saved content, or drop to the lowest available package so that I could continue my access.