Well, the 60 year old aircraft wins this one:}

Oh Your 737-800 is RNAV 5 with HDG ALT and VOR/LOC ?

No it is not, but it still is RVSM and I have yet to follow a flightplan from start to finish in Europe.
Direct a VOR or follow a radial will work fine , if not vectors are provided for 5nm + separation.
Par Problem

Remember Sonic
Once air -borne MEL and all that jazz is history
We actually got to destination in the old days as well.

Oh great, so if I lose my RNAV capability I just shut up and go to destination without advising ATC I have lost my RNAV capability. Thanks for the tip.

ICAO : "When an aircraft cannot meet the requirements for either P-RNAV or B-RNAV, as required by the RNAV ATS route or procedure, as a result of a failure or degradation of the RNAV system, a revised clearance shall be requested by the pilot."

It's a complex world we live in my friend.

Indeed
It is indeed. I have had total FMC fail on the 738 3 times and once HDG is selected and my friend in the RH seat is deeply and intimately engaged with the QRH and I have concocted a plan B for the next few FIR boundarys , Murphy has let the old Boeing reset itself and we order some coffee.
And for the rest of the trip we pay a bit more attention to which country we happen to be in.
PS
Still not so keen on Beirut raw data, not quite the place for large navigation errors!
I will practice in Europe
Thanks

Applying MELs' airborne? Pretty sure you mean 'Apply QRH procedure...'

Applying MELs' airborne?

No, just gathering info. Can it be repair at destination if that's a No Go??

And also if the item is a no dispatch, there could be one or more good reasons behind it. Always worth a bit of brainstorming, especially if that happens during taxi out... 5 mins before we would have been stuck at the gate waiting for a repair, now we are going to fly 10 hours with it ?

MEL surely would leave the aircraft u/s in Beirut

What if BEY was home base? This was never stated by the OP.

If You have preset some navaids via back-up tuning and then deselect the NAV key You can subsequently have them ready for use once the NAV key is selected again (dual FMGC fail). About 20+ years ago that used to be the procedure in my airline in case of dispatch with 1 FMGC INOP, but that was mainly due to the fact that the airline was relatively new to the Airbus 320 family and coming from conventional liners there was still this "I don't trust You" mentality that luckily quickly disappeared with some Airbus expertise. I believe that the guys You mention are either low experienced on type coming from 737s-like aircrafts or just simply over zealous. Aside of not being an Airbus procedure, statistically speaking it is more likely to have an engine failure on takeoff than a dual fmgc failure.

raw data as backup from hard tuned stations can be helpful for other situations/malfunctions. maybe that's the their reasoning behind that?