What you are referring to is called capillary condensation [1]. When you have a hydrophilic surface with thin capillaries or small pores, they can pull water from the air below 100% RH. However, this process requires an enclosed space with a very small radius and the air-water interface is always concave in this case (it's just how capillary forces work).
Forming a convex surface, on the other hand, requires an at least slightly hydrophobic material and produces a positive internal pressure. This is a key difference, because condensation into a hydrophilic pore is favorable in terms of free energy, while condensing onto a hydrophobic surface is unfavorable (unless you have a supersaturated vapor).
> Theoretically speaking, you can have a material that somehow absorbs high moisture from the air but has microscale properties that promote creation of droplets then somehow these droplets are separated from the rest of the air
That "somehow" is what makes the paper's claims impossible. The water condenses spontaneously into the pore because it thereby lowers its free energy. Extruding it onto the surface is then even more unfavorable than direct condensation. Unfortunately, no passive system can achieve this feat, no matter how cleverly nanostructured, as it would go against the arrow of increasing entropy. You need an external energy source to drive that process.
Thank you, this is a very clear explanation for me.
It filled the critical gaps in my intuition that I didn't have the brain cycles to formulate hypotheses against.