Debatable, but I'd say yes.
According to page 439, a simrig can record "experience data (sensory and emotive)", and lists this as its main feature. A direct neural interface on the other hand "connects your brain to electronic devices" (page 222, DNI), so I would personally allow recording of sensory input (sight, sound, smell, taste, and touch) with nothing but a DNI and a connected commlink.
To my mind you wouldn't be able to play that latter recording back in full sim mode, however, as a simrig would definitely be needed for that. I'd also say that the smell, taste, and touch components of a non-sim recording would be of limited usefulness, except perhaps for later analysis or something. No idea how I would rule those, but the sight and sound as interpreted by your brain, sure.