No, the point I was trying to make is that board intended for use as a tile backer board in showers will be highly resistant to moisture, and that means it's won't deteriorate or lose it's strength/rigidity if it gets wet. This is important since any loss of rigidity of the tile backer board is going to result in the tiling bending, and that results in the grout lines cracking.
And, of course, grout lines cracking leads to the tile backer board getting wetter still, and the situation becoming analagous to that of a snowball rolling downhill.
The grout is water proof. It doesn't deteriorate at all if it gets wet. The problem is that cement based grout is porous, and the mildew spores will grow in that wet porous surface just like stuff will grow between the rocks on a rocky beach. It's the grout itself that makes mildew hard to clean off of mildewed grout just like it's the rocks themselves that make it difficult to clean an oil slick off of a rocky beach. By sealing that grout, you prevent the water from being wicked into the grout (one way or another, depending on the kind of grout sealer you buy), and that in turn prevents mildew from growing IN the porous surface of the grout.
If cement based grouts weren't porous, they'd be no more susceptible to discoloration of their surface by mildew than the glazed ceramic wall tiles. Epoxy grouts aren't susceptable to mildew precisely because they don't dry porous like cement based grouts do (but epoxy grouts aren't as user friendly as cement based grouts to work with, and may not be appropriate for use by a DIY'er tiling something for the first time).