Your insurance company is correct that colliding with an animal, such as a deer, is covered under the comprehensive portion of your auto insurance policy. Under most circumstances when a claim is made to this part of your policy the deductible amount (which you chose when starting the policy) will apply.
With regards to the information you received from your friends and the body shop it might be that certain insurance companies will allow for the deductible amount to be waived for this type of incident. Speak with your insurance agent to find out exactly what your insurance company's rules and guidelines are.
Since state laws differ, it is possible that your state has laws in place that reduce or eliminate your deductible amount when your car is hit by wildlife. You might contact your state's insurance regulatory body to find out if this is true for your state.