Asking your agent the questions you posed is not a bad idea. But adding, or being added, as an “additional named insured” is a very common practice in many circumstances.
I have two tenants that lease property from me. My company, Travelers, requires that both carry policies with a minimum value and both must name me as an “additional named insured” under their policy. This does not, in any way, excuse Travelers from defending me in the event that a claim is made but it does mean that Travelers may not be primarily liable for indemnity. In short, it’s a partial “shield” for Traveler’s interests given that they did not write the policy on the tenant and have little control over the tenant’s activities.
G.