Yes, no, I don't know. The heated exhaust gas oxygen (HEGO) sensor is used to establish fuel air ratios on some vehicles. You could run rich or lean. I've personally seen a vehicle with long term HEGO fault that caused continued preignition to to point that the bottom of the pistons broke off past the rings. Vehicle overheat... no. The pistons broke. Hint: that's a mighty expensive repair.
Recommendation. Get vehicle to design intent. Repair or replace all inoperable sensors. They are pretty cheap to replace. If you are in the USA Autozone has an awesome tool in the free tool loaner program that makes this a ten minute repair for the Do It Yourself person. The biggest problem is the repair is best done on a hot exhaust. You need to be careful to not burn yourself.
I will say, I'm a bit confused by your posting. What, pray tell is a FAP filter? I have no clue what that is. Best practice is to define mystery abbreviations When First Used (WFU).
You also mentioned the dealer "programming" the engine computer. That sounds pretty odd to me. In my experience (not with Peugeot, but with a United States based Manufacturer) engine computer reprogramming is a mighty rare event. It does happen, but not very often.
Its more likely that the dealer reads stored fault codes (OnBoard Diagnostic (OBD2) codes, and erased them. Is that a possible interpretation?
I wouldn't necessarily call either service team dishonest... Best action for the long term reliability of your car is to fix defects to manufacturer's design intent.