You want the smart ass answer of the possible most worst and usual scenario's?
Smart ass: Yes they can. You bought the device and you're on camera
Most worst: Yes they can. Everything you do is actually recorded somehwere someplace.
Usual: People write their dvd's with Nero. Nero leaves traces on the dvd. The dvd itself has a serial number, but it's usually not recorded.
Is there any software that removes location of burn/hides the origional file location/location where files were created or downloaded to.
Leave no traces in nero and use sandpaper to remove the serial number on the disc.