True, the resulting soap does not have any harsh chemicals if the soapmaker has done things correctly. That does not mean that chemicals were not used in making the soap. It just means that there are none present in the product you are using since they have all gone through a chemical reaction with the oils to create the wonderful soap molecule. If anything, there are more oils present in the formula than lye to ensure no harsh chemicals are free (also known as superfatting soap).
What about glycerin soap? Hmmm…well…glycerin soap is not really soap, it is a syndet (synthetic detergent) to which glycerin is added. So it is made entirely of chemicals, with maybe an addition of oils in the end so that the bar is not too drying. But the base is 100% synthetic - not 100% glycerin as some would have you believe (glycerin is a viscous liquid not a solid).
How do I tell the difference? Is the soap wrapped in plastic that looks like cling wrap? Then it's probably glycerin soap. It is also notoriously short lived in the shower due to the high content of glycerin it contains. Another tell sign is the ingredient list...if it starts with glycerin and continues with other oils and fragrances but does not have any indication of lye (sodium hydroxide) or other hard to pronounce chemicals then it's probably glycerin soap - and mislabeled to boot.