Ambient humidity affects all porous materials. Hydrophilic materials - particularly cotton, linen, paper, rayon (such as in bandages), absorb moisture from the air. They will not become more moist than the ambient humidity, however. If the air in your home is 12%, then given time, all porous materials will absorb that moisture until they reach parity with the air. Ditto for outside. Paper towels stored in a shed will have significantly more moisture than those stored in a house. Paper towels from a warehouse will be more moist than those in the store. Ironically, those that move faster from the store can be more moist than those that sit on the shelves longer because of the drying effect of air conditioning. In a similar way, those from one store sold near the freezer section can have more moisture than those further away (but this is due more to condensation than the truth that % humidity will be higher).
What ever the moisture at the production facility is irrelevant to the end use as regardless of the moisture content, the product will shed or absorb water until it reaches parity with ambient air. This is also true of lumber and, for that matter, all porous materials.
As to using it on guns, I wouldn't because of the reasons posted. Recycled paper is worse than virgin paper (and recycling paper is significantly worse for the environment than virgin while providing no protection for trees what-so-ever) because it does contain impurities that will damage finishes. This is also true of recycled cloth.
But another reason to eschew paper towels is that they can leave cellulose fibers scattered about. An old shirt or, frankly better in my opinion a good set of old boxer shorts, is far better for cleaning guns. Just make sure it hasn't been use for other cleaning that might have picked up fine grit -you'd defeat the whole purpose then.