Well, I have two Custom spec LS models on order.
Both with one piece Honduras mahogany bodies and necks, one with an Ebony fretboard and one with a Madagascar rosewood fretboard.
I asked/begged for slightly wider thicker chunkier necks, I was told there is only one current neck shape/width/thickness and they can't (even with a Custom order) make me a chunkier neck...and I offered to pay extra if they did.
However they did say that the neck might turn out slightly chunkier than the specs/measurements they gave me (the measurements I posted above), but that wouldn't be because I requested it, it would just be by chance.
Keep in mind, the specs I posted include fret height, so higher frets could measure as a thicker/deeper neck.
My favourite spec upgrade which they willingly do for me on all LS models is thicker frets, Dunlop 6100/6105 (SBB-215)...once you play a LS model with these frets you can't go back to the thinner frets, these frets rule!
It appears their CNC machines have one neck profile programmed, but as Reborn mentioned varying degrees of finish could account for slightly different final specs.
For me personally I love the current neck profiles, I asked for a chunkier neck because that's what my customer requested.
He loves his 2013 LS100F but said it would be nice if the neck could be slightly chunkier, but he's more than happy if it turns out just like the 100F.