I'm afraid your mechanic is correct. Cam phasers on the ill fated 3V Tritons has been an issue since they came out. Thankfully they are now gone in the F150. Having an issue with the cam phasers means the engine sounds like a diesel at idle. The noise will not effect engine life per Ford TSB. I would suggest getting a code reader on it though. If you've never replaced the cam position sensors on that 160,000 mile engine, I can assure they are shot and MIGHT be the problem. You are talking an easily replaced part on the front of the engine, each side at a cost of about 100 bucks each. It's pretty much a plug and play kinda part.
Just as a FWIW, if you haven't replaced the plugs in the Triton 3V, make sure to have a Motor Vac service done on it BEFORE having the plugs changed or expect a HUGE bill. Those are the multi piece plugs that are prone to break off in the heads. The MV service gets rid of a lot of the carbon around the stem of the plug that creates the issue. ALWAYS use Motorcraft parts on that engine including the PCV or expect issues. Yeah, it's a finicky engine.
The F250 is a 2V engine and not the same head design.