@FaulkSF I see what you're saying about any official's calling a safety foul, but are you also saying/suggesting/implying that a non-safety foul outside an official's zone but seen by that official wouldn't be called?
That's correct. You may have two officials working the same zone dependent on the play, but usually it's deferred to the official with the zone and key.
E.g. An offensive tackle or tight end formation when no WR is lined up is the responsibility of the flank official (either line official). While it may be in the referee or ump's vision, it's the flank's key they are focused on. The ref is normally keyed on the QB, and the ump has the middle of the line GCG.
Holding would normally be called by the flank on the line by a WR or TE. Unless of course the hold occurred closer to the QB on a pass play. You may get two flags there (flank and ref).
Sometimes multiple officials will share a zone. E.g. if the TE or WR runs a 5 yard route up the sideline, the flank and field judge could both flag as that is the shared zone. The flank will pass off the WR/TE after about 5ish yards, and refocus on the TE/T/RB in play on that side.
The latter was a failure of the flank to refocus on the RB in the Rams - Saints game that resulted in the non-PI call. The flank was caught ball watching Brees.