Sadly not true. When a major assembly such as a gearbox is refurbished, some components will be replaced as a matter of course - precisely which ones will depend on the policy of the refurbishers. Other components will be inspected, and if found fit for further service, reused.
In the case of a gearbox, it's likely the bearings, seals & synchro rings will be routinely replaced. The cogs & layshaft will be inspected for missing or chipped teeth & dogs, but only replaced if found to be damaged.
This means your recon 'box may have pairs of gears where only one has been replaced, and used gears & shafts running in new bearings - both well known causes of gearbox whine.
Now I seem to recall the OP saying the car couldn't be returned after fitting the replacement 'box because it was whining....
Please don't misread what I'm saying here. Reconditioned major components can be a cost-effective way of repairing a secondhand car and often give many, many years of good service - but they're not the same as new, and the way in which this incident has been handled IMO falls far short of what a new car customer could reasonably expect.
I certainly wouldn't consider arson as a way forward; but I might at this point be contemplating litigation if the dealer wouldn't offer me a replacement new car.