Can my auto insurance deny my claim because they think I was using the vehicle for work related purposes?

I am unemployed and do not receive a paycheck at all. During the accident, I was on my way home from the plumbing supply store after picking up a water heater. My father owns a plumbing company but I was picking up the water heater without his permission and giving it to a friend which had nothing to do with work. All supplies and equipment that is picked up for the plumbing company are picked up with his fully equipped plumbing vans which are registered under the company. My truck is a luxury pickup that does not contain a single tool and is obviously not used for work at all. It is spotless and does not contain a single tool. Please let me know if they have a case to deny me.