Well, the title may seem really odd. But, yes, there have been lately many contradictions to the fact that glycerin draws moisture from our body and not from the air. Here, you would find one of the articles which states such a claim.
Glycerin is a natural by-product of the soap making process and is separated for soap to be used in the lotions and creams. 100% natural glycerin is highly concentrated and is not considered good for our skin as it can cause blisters by drying our skin. But, the glycerin which you get in the markets is not the original concentrated glycerin but the diluted glycerin which is good for daily usage.
And, when you use glycerin, you mix glycerin with other ingredients and then use it on face (or for any skin care). Interestingly, a mixture of glycerin and rose water used to be a favorite moisturizer in the olden days when there were no body lotions available. And, your grand moms will swear by the remedy. So, basically, it does not dry out our skin. Instead, it acts as a humectant just like honey and provides a protective covering instead of just coating our skin like Vaseline does. So, if you are buying a product which says it has glycerin in the top of its ingredient list, do not worry, because it is not the original glycerin but rather a diluted form of it. And, it would not cause any skin irritation or have any drying effect.