In my experience viable pollen does not need moisture to 'stick' to surfaces. I have had anthers accidentally touch and pollen stick to dry styles, filaments, petals and sepals. I tried a test just now and had viable pollen 'stick' to dry petals, sepals, daylily leaves, filaments and styles.
I tried a different test as well. I opened daylily buds that were several days away from opening by themselves (a test that Sue suggested). The buds were approximately half-size and tightly closed. I used pollen expected to be viable and had no difficulty with it 'sticking' to the stigma. There would not have been any stigmatic fluid or any other liquid present. The pollen adhered to the dry stigmatic surface.
Whenever one does a garden test of the pollination process one has three possibilities. Any problem present may be caused by the pollen, by any part of the pollination process due to the pistil/female tissues or due to both.
Stout pollinated his flowers and then collected the pistils. He examined those pistils microscopically to see how far the pollen tubes had moved in the channel. To conclude that stigmatic fluid dried and blocked the growth of pollen tubes one would have to repeat his experiments and examine pistils microscopically and see a plug at the opening and no penetration of pollen tubes into the channel. Without doing that or something equivalent we are left with what are guesses or assumptions about what is happening.
If pollen is not sticking to a stigma, whether the stigma is obviously moist or seemingly dry, possibly the problem is not with the stigma but with the pollen?
The photo is of an immature (by several days) pistil (from a bud cut open today) and pollinated with viable pollen, showing the pollen sticking normally to the dry stigma.