Valen, are the soaps in question being hand-made in the same way that we on the forum normally make our soaps, or are they producing their soap from pre-made, extruded soap flakes/noodles that have had their naturally derived glycerin removed so as not to gum up the extrusion machinery? If the latter, it's possible that the reason why glycerin is mentioned on their label is because they add some back in when shaping/pressing the flakes/noodles into bars.
If the above is not the case, though, and they are making soap in the same manner that we here on the forum do, it still doesn't necessarily or automatically mean that they have added any extra to their soap beyond the amount that is naturally produced as a by-product of saponification. Some people just choose to include it as part of their ingredients list for no other reason than to add label-appeal for increased sales, even if it was only naturally-derived as a by product from saponification. Unless you have actually talked to someone from the company in order to confirm or deny the reason for it being on their label, though, I wouldn't assume anything.
If they make their soap in the same manner as we do, I daresay it's more likely (at least to me) that they are probably just super-fatting their soap fairly high. For example, I make super-bubbly 100% coconut soap with a 20% superfat and it's not drying to me at all.
Also- you mentioned some kind of milk being listed on the label as well, which also helps to increase the overall super-fat. Depending upon how much fat is present in the milk, and how much is added, it's not out of the realm of possibility to actually boost a normal super-fat up by 10% or so.
Although glycerin does feel nice on the skin, adding extra to bar soap can make it somewhat soft and sticky, depending on how much extra is added.
For what it's worth, I make a shave croap with 20% ppo added glycerin, which is perfect for that kind of soap. It's somewhere in-between hard soap and a soft cream-like soap. I personally would never use that much in my regular bar soap, though.
Do you find the soap from that company to feel soft or sticky?