Why whole milk?

I've mentioned using whole milk to stop a skin reaction in other posts.  Since this seems to be a little known remedy, I thought I'd elaborate on it.

The very first class I took for aromatherapy was a safety class taught by a registered nurse/aromatherapist.  It was her suggestion to use whole milk to calm a skin reaction (contact dermatitis) to an oil.  She was right.  So far, I've successfully used whole milk to stop a reaction I had to an oxidized oil, to flush sunscreen out of my grandson's eyes,  and to stop minor skin reactions of three highly chemically sensitive clients who did wrist tests of ingredients prior to formulation of individual products.  

In each case, whole milk stopped the reactions!

I've searched online to try and understand why milk has this effect, but haven't been able to find anything.  I finally did find a website (https://www.allure.com/story/how-to-deal-with-red-irritated-skin) which mentions a dermatologist's 
(Amy Wechsler) recommendation to apply a cold milk compress to a contact dermatitis reaction to calm it down.  (Edgar, 2015)  Dr. Wechsler explained that the fats in the milk have anti-inflammatory properties. 

Given my experiences, I wonder if there's more to it than that.  My hypothesis is that, in addition to the anti-inflammatory properties, the lipids in whole milk are able to absorb oil molecules more readily than the lipids in our skin.  With the epidermis providing a barrier that slows the absorption of substances, perhaps it gives enough time for the milk to pull the oils back out.  Since milk is also an emulsifier, it could be that it  disperses the oil molecules and washes them away.  The combination of absorbing and dispersing the 'offending' molecules would remove them from the skin.  Once those molecules are gone, the immune system no longer has a reason to react.  

Can I prove my hypothesis?  No, I don't have the equipment.  Can I prove that whole milk can stop/calm a skin reaction?  Yes, by documenting it's use in cases of contact dermatitis.