So if you heat the air, you heat the water vapor. Both will expand. Volume increases and density drops. Total mass remains the same. The only way warmer air could hold more vapor, would be if you are also referring to a greater total mass of air. So their stunning scientific observation is that more air can hold more vapor ?
The only thing that makes sense to me is that moisture in this context means liquid water. Warmer air has more volume and can thus hold more liquid water. But again, you can only get more liquid water in air if you increase the nuclei catalyst (ex. - Cosmic Rays, Silver Iodide) that stimulate the conversion of water vapor gas to liquid water. And I am guessing that you can also get more by cooling the water vapor gas and just converting it into a liquid.
No. If you heat the air, and there is liquid water available, the air will take up water from the liquid phase into the gas phase. The scenario you describe is where there is no liquid water around. In that case, the CAPACITY of the air to hold water vapor increases, but the amount present does not.
"So their stunning scientific observation is that more air can hold more vapor ?"
Is correct.