rear end whine

[84LX89GT]

I don't know why the mechanic only replaced the bearings in the rear axle, a whine is caused by the ring and pinion wearing incorrectly or excessively wearing on the thrust face. A rumble or grinding would be bearings.
The '02 and up explorers have had alot of bearing and ring/pinion problems, there has been several special service messages and technical service bulletins on axle whine. for awhile Ford was having us (i'm a ford tech) replace the whole thing. Now there is a kit that includes bearings and the ring and pinion set with all the shims needed to install the ring and pinion set to the correct clearences. ford tightened the specification for backlash between the ring and pinion teeth and i believe changed the manufacturing of the gears.
Alot of times if you go to the dealership and request a different service advisor or request a different technician work on it you may have better luck. Or you could also go to another dealership altogether and see if they do any better.
Good luck,