The rate that is charged for a certain life insurance policy, from a certain company, at a certain health rating, will be the SAME even if sold by another AGENT.
Rates among life insurance COMPANIES, however, are DIFFERENT. That is where shopping can help, because different companies have better rates for different age groups, health conditions, and types of policies.
And that is also where your agent can help you get a better rate. Some agents have more options to offer; some have more experience; some understand health conditions or product types better.