The thing in that photo is quite porous. Also paper is very penetrable by water, so it wouldn't be too surprising.

But, well, if it's that simple, just soaking cellulose acetate in NaOH should have a huge number of applications. Maybe even more interesting than this 3D printer.

(Gotta try this at home later...)

Maybe it doesn't penetrate through the walls entirely - perhaps just the outsides? Sort of analogous to constructing a wide brick wall with the interior filled with rubble?

Sounds like they soak the print in a NaOH solution. I imagine if the material is porous enough to evaporate acetone, it's also porous enough to absorb a NaOH solution.

Just in case someone else gets bogged down in chemistry, NaOH is better known as lye or caustic soda.

They called it Sodium Hydroxide in the article as well. :)