Microsoft eventually got this right, IMO, with the X360.
Yes, downloaded content will only work on the original console it was purchased from (by serial number) or the Xbox Live Account. However, I suffered through no fewer than 3 red-rings of death from 2006-2009.
The first console came back with a different board, different serial number. My content would only work by logging into Xbox Live. Royal PITA.
Second console came back but MSFT allowed the content to be re-downloaded and authorized on my new serial number. While a royal pain, after re-downloading everything, it would work offline again.
Skip ahead to about 2009-2010 time frame. MSFT finally put the option to TRANSFER your content from one box serial number to another on their website. It is restricted to one use per 6 months, so it cannot be abused, but lets the user move their content to another console if their old console is broken, sold or they purchase a newer model. I did this in 2011 when I upgraded to an S-series xbox.
I personally think this is a fine compromise to DRM. Online connection always authorizes the content. Offline is allowed by serial number of original purchase. Serial number of primary device is transferrable to another console at the user's discretion (with some restrictions, once per 6 month period, etc).
Without that last feature, however, I consider the DRM draconian. I took my originally repaired console with me one xmas to my in-laws, and found I couldn't play my Oblivion game because my saved game had used Knights of the Nine and without internet access I could not play. However, I could load an older save file that was created before I had any DLC content for that game. My in-laws at the time only had dial-up modem (56K), so it rendered most of the content useless.
If this is the future of gaming, I will not be participating. I will punt on the next Xbox and especially if it has no backwards compatibility. I think it is reasonable expectation from consumers that a new device should at least be able to play games from it's predecessor, but not go back further than that. But if that is what happens, so be it, there is plenty of good (OLD) games I would like to play again via Steam or GoG.com on my PC.