Hiya, I've been dealing with the same issue, (I am the landlord) and I think what your landlord was referring to is to be added as an additional interest party, NOT a recipient. This will tell them if the policy lapses, or cancelled..etc.. and if having tenant insurance is a requirement for leasing their property, they need to know you really have it.
This leads us to the question, WHY do landlords want tenants to have renter's insurance....
In my research, one reason that hasn't been mentioned, (and to me, its THE reason landlords want tenants to have renters insurance), is because if you ever have to find alternative lodgings due to a fire, flood, or even a simple repair that might require a few days away, your landlord is legally obligated to prorate your rent, which they can insure against. What they can't insure against is if the alternative accommodations are more then what you would have paid for rent, the landlord would have to pay for this out of their own pocket and this could add up quickly. As a landlord, this might bankrupt me b/c I'm not a rich corporation, just an average person, and I'm probably poorer then all my tenants. Anyway, this would also make finding alternative lodgings that your landlord "approves" of very difficult. You might end up miles away from your home, or the accommodations are just ...well..... "yucky".Your tenant insurance would cover this, plus you could pick a nicer place closer to your home! I wish landlord insurance policies would cover this, but they don't seem to. Or at least I haven't found any. I think they offer rent loss OR alternative lodgings coverage, NOT both.
So weird.