I guess the equivalent to a sbf on the Nexus is flashing a stock image using fasboot. Now this I have NOT done in quite some time. When I find the time to back up everything I might try to flash the latest 4.0.4 build from Google and see if it happens there before flashing any custom roms and then report back, but honestly it's so fast to just clear data in download manager I'm not sure it's worth the hassle at this point other to just see if it works and report back in the name of Science. I don't remember if flashing via fastboot wipes the sdcard partition or not. I "think" that it leaves that partition alone if memory serves
Edit: I think I might try to debug the issue first as I'm quite good at that being as I program for a living. See if I can download a lot to maximize it out and get a logcat of what's going on. Also should see if any third party browsers exhibit this behavior since I've only been using Chrome and Stock. Also maybe completely un install and remove all traces of DownloadManager and install a different fresh copy. Any other ideas to troubleshoot? Something is getting corrupted in Download Manager and having a look around in the data files might find useful as well. I'm surprised though that I haven't seen anybody else report this issue.