ummmmm , you know it is actually medical correct to run the burn over cold running water for 5 minutes , to prevent any further or severe damage.
At my place we all do the same thing run over cold water , and then spray an anticeptic to kill off any bacteria that or you can
wash the burn and apply aloe. But thats all you can really do.
When your on the job working 115 dishes and you burn yourself , you will most likely go run some cold water on it , and go back to work before doing anything else. Its not that we are stupid , we just cant let the crew down.
Now if i burn myself severly , then obviously i will seek medical attention no matter the cost ,
2 weeks ago i dropped boiling water on my foot , i quickly ran to private space in the kitchen while taking off the shoes , took of the socks , ran cold water on it with a hose , sprayed anticeptic and in 6 minutes tops i was back in the stove boiling water again XD.
Trust me if it was something extremely severe like lets say.... hot oil then the first thing i would do is run to the hose , run water over my feet , and tell my chef im clocking out , and that is that (obviously the burn would have to be pretty sever , painful and intolerable ) !! If the chef is smart enough he will demand you to leave the kitchen before you even ask.
Now in you situation the commis splashed oil in her hand , and she did the right thing in running the cold water , now if she obviously felt she could handle the burn and it was something tolerable i guess its her risk , but the manager and or chef should have at least asked if she wanted medical attention...
Obviously the situation is relative , because most chefs are stubborn and wont leave the kitchen because of a burn , ( at least i dont , if i think its tolerable ) but it is the responibility of who ever is in charge to at least ask if one desires medical attention , if the answer from the employee is a no , i would probably keep an eye on said employee just to see if they arent attempting to play the hero. Aside from that the answer is....sure you can do other stuff to a burn , but the fastest , easiest ,and most common would be running cold water over it.