After reading an article highlighting that personal data may be recoverable on console hard disk drives even after a factory reset, I took the precaution of running DBAN on my Xbox 360 drive before selling the console, as per the recommendation on various websites.
Unfortunately this had the effect of making the disk unusable in an Xbox 360, due to something called a Security Sector that got overwritten. It would appear, then, that the trick is to back this up before using DBAN, then restoring it afterwards. Too late for me now, though – boooooo!