Mokuton is a combination of water and earth natures. Though no one has utilized it without the direct injection of Hashirama's cells, indicating that it is indeed a different type of Ninjutsu which only Hashirama's cells work with.
The same cannot be said about Lava Release, Dust Release or Magnet Release, as there are several users who don't seem to be related, thus have different cellular structures.
There is literally no such thing as "natural element." Because elements are part of nature. But this Ninjutsu isn't really just chakra based, as it canonically has created life, which will continue to create life when filtered with Yang chakra (Naruto's KCM Cloak)- as no other Ninjutsu has. I would assume it is partly a Yang construct because it creates life from nothing, but who cares enough to go that deep into it? It's just too hard to figure out.
The only real explanation, as stated canonically, is Hashirama's cells are supernaturally filled with life force (just like Karin and Nagato), as and such, his chakra has the ability to create life (Mokuton), his body can recover faster (Zetsu durability), and can control Natural Energy (SM) and his normal chakra (like Tsunade's medical ninjutsu control) with ease. It's also implied that his chakra is of it's own caliber when Orochimaru used it to increase the restraint and effectiveness of Edo Tensei.
I have to agree that it cannot be absorbed, but attempting to absorb it will not turn someone into stone: that only works with Natural Energy (SM)- not nature transformation (Mokuton). The one absorbing would simply be crushed by the wood.
Now if he tried to absorb SM Hashirama's Mokuton- then we can argue that he'd turn to stone and be crushed.
I'd like to see whether or not The BD thinks Magnet Release (KG), Explosion Release (KG), Gaara'a landscape-obliterating sand wave (KG?), Deidara's C3 Explosion/Clay (KG/Hiden), Shikamaru's shadow (Ying-Yang/Hiden), Ma/Pa's Frog Call (Sage Art), Super-expanded Choji (Hiden/Calorie Control), Kimimaro's Bone Forest (KG), Ino's Mind Control (Hiden), Naruto's Frog Kata (Sage Art), Onoki's/Mu's Flight (?), Onoki's Weight Control (Doton), Onoki's Mobile Golem (Doton), Kitsuchi's Sandwich (Doton), Kitsuchi's Moving Earth Core (Doton), Mu's Camouflage/Body Splitting (Ninjutsu/?), can be absorbed entirely as well- as they also are formed from chakra.
Not everything controlled or created from chakra can be absorbed. It simply isn't logical.