Do you know if there is any vapor barrier behind the wall? CBU (cement backer unit) is NOT waterproof, but it is a good backer for installing tile. You could have more problems behind that wall. Is the tub also used as a shower? If not, then that isn't as critical. Terry's site is great for plumbing, but I think you get better info on tiling over at his friend's www.johnbridge.com
Glazed tile is fairly waterproof, but the grout isn't, and water will penetrate that too. Thus, without a vapor barier behind the wall, the structure could be rotting. Note, the tile council of America recommends caulk between changes of plane or changes in materials, so, the joint between the tile and the tub should have been caulked.
Is there any way you can look - maybe poke a hole in the wall in an adjoining room to take a look around inside. That may help you determine what the wall is made of and it's state; much easier to repair that than the tileed wall. It may help you decide what really needs to be done.