Most insurance companies' normal private passenger auto policies do not provide coverage if the covered vehicle is being used to deliver property, i.e. pizza or people for a fee (salary, tips, etc). Coverage can thus be denied if an accident occurs while the personal vehicle is being used to deliver items such as pizza.
There are some states that might require the insurance company to allow the state's minimum insurance requirements to cover a private vehicle whether it is being used for personal or business use. So you can check with your state's insurance regulatory body to see if your state has such laws.
If state laws do not require your boyfriend's insurance company to cover the incident then he will likely need to get a commercial or business policy on his vehicle if he continues to deliver pizzas and wants have his vehicle covered by insurance.
As for the damages, if the other person took responsibility for the accident, in most states your boyfriend should be able to put in a claim with their insurance company, but this would not be covered under your boyfriend's personal auto policy.
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Comment Update: The issue here is if the accident is covered by the responsible party OR if the boyfriend's personal policy will cover it. This typically is not covered under a personal auto policy. CarInsurance.com does not currently have a carrier that will cover this under a personal auto policy. Typically, no personal auto policy will cover "delivery." You will need to purchase a commercial auto policy. | 
