Yep, that's my understanding too. The shorter the carbon chain, the harsher the cleanser -- more irritating, stripping, and drying. That's especially true when you get down to lauric with 12 carbon atoms (C:12) and shorter. I've mentioned butyric C:4, capric C:10, and caprylic C:8 fatty acids -- you can see they're even shorter than lauric acid.
Another aspect to consider is the water solubility of the soap. A soap that is more soluble in water, all other things being equal, might be more irritating to the skin than the same soap that's less soluble. Example might be soap made with NaOH (less soluble) compared with the same soap made with KOH (more soluble).
I've wondered if the higher solubility of olive oil soap is possibly why some people find olive oil soap to be drying to their skin, despite the common wisdom that it's one of the milder soaps one can use.
