If I had just hit and killed somebody, I'm not sure that my first concern would be opening the cowling to find out where the oil had come from but then that might just be a personal thing.
Some people can act very oddly or say unusual/inappropriate things immediately after an accident or other situation. They're on an adrenalin high, they're highly stressed and subconsciously "need to do something". A friend of mine was very badly injured after a car travelling at high speed on a country lane hit and killed her horse while she was riding. When the police arrived, the driver kept asking if his after-market fog-lamps would be covered under insurance...
Pilots may be in a better position than others when dealing with high stress, high workload situations, but checking the oil may have just been something the guy did because he couldn't do anything else - a displacement action maybe.