Call me niaeve but what the F@#k has the CEO of a commercial organisation got to do with passport and immigration procedures.
Surely all he can do is have your residence permit cancelled and when that happens doesn't the immigration department give you a standard amount of time to leave the country, I think it is 2 weeks in Bahrain.
If the CEO is however ordering the immigration department to not grant this then maybe that is the problem.
Qatar authorities should not allow him to override procedures. Even in Saudi now this practice is being stopped.
The only people who should have the right to throw you out of a country (deport) should be the courts as it is in Bahrain.
However it does seem that Qatar Airways do need someone strong to be their HR manager, maybe an Al Thani!!
Personally I travel between Bahrain and Qatar a lot and having tried Qatar Airways once I am sticking to Gulf Air and the simple reason is that Gulf Air do not try to do a cabin service on such a short flight. On the Qatar Aircraft it is a total panic and we ended up circling at Bahrain until the Cabin Crew had secured the cabin.