The New York Jets have explained the presence of the cameraman.
Stating that the man “works for Jets TV and shoots footage for our team programming” they believe they are not violating any rules.
In fact, the Jets point out the NFL’s policy on sideline media that permits “[c]lub video crews and video crews from television stations that produce and telecast club-licensed programming (e.g. coaches’ shows, team magazine-style shows, etc.) may also be permitted to have a camera on the sidelines to shoot footage for those club-licensed programs only.”
Such personnel are required to wear lime green vests. The man shown with a camera was in a lime green vest. (see pic below)
It’s a very weird rule and seems like it requires the honor system and coaches to police themselves; something that cannot always be trusted in the NFL.