JWhy exactly should a gas (let's say O2) need to dissolve first? In a hypothetical situation, a gas should be able to pass through a permeable membrane without much issue. Therefore, I would argue that a gas could diffuse across a dry membrane before finally diffusing into the blood.
A gas can pass through a (dry) membrane, certainly. But it is well known the moisture level can impact the rate of gas transfusion across many polymers, particularly biopolymers. In the presence of water, many biopolymers (which tend to be rather polar) swell considerably. The swelling increases the rate of transfusion for a lot of obvious reasons, the simplest of which probably comes down to available void volume.
This has implications beyond the biological. In packaging technology, the oxygen transmission rate (which is important to, say, shelf life of packaged foods) of synthetic polymers can be highly dependent on the relative humidity. A popular polymer for food packaging is EVOH, which is basically polyethylene modified with varying degrees of OH groups. EVOH has fantastic oxygen transfer barrier (low oxygen transmission rate) in the dry state, but the barrier lowers as the %RH value increases - almost two orders of magnitude, as measured by OTR. This sensitivity depends on the OH content of the polymer - higher OH content makes the polymer more prone to swelling, which increases the functional oxygen transmission kinetics. You can compare this to the OTR properties of LDPE, a completely nonpolar polymer, which has a very poor oxygen barrier due to its high porosity, but the OTR value is completely insensitive to %RH.
See the image on the following website:
http://www.evalevoh.com/en/eval-properties/barrier-to-oxygen.aspx.
Because EVOH is such a good polymer in the dry state, a common practice is to coat it in a secondary layer of a hydrophobic polymer to insulate it against water that would swell it and decrease its functionality. Because it is so hydrophobic, the water vapor transmissivity of LDPE is very low, and so this is frequently used as an external barrier layer. So you might have a trilayer film - a single layer of EVOH that provides good oxygen barrier, sandwiched between two layers of LDPE that protect the inner layer from water. This gives you a film that has an excellent oxygen vapor barrier, even if you are storing a very moist food in close proximity to it.
Because biopolymers tend to be more polar than, say, polyolefines like LDPE, they often behave like EVOH. They may have very low oxygen transmission rates in the dry state, but absorb significant quantities of water, which enhances the OTR by orders of magnitude when wet.
This is a simplification of course. Biological membranes are very complex, and their chemical structure may also change in the presence of moisture. I'm no physiologist, but if I were to guess, I'd guess that moisture-swelling has something to do the oxygen transmissivity of alveolar membranes.