The only reasonable objection which occurs to me is if the installation involves putting unsightly new wires across the building. However so few phone lines need that these days that I think it's more likely to be that the LL just doesn't want the (perceived) hassle of having to have the phone cut off and chase Ts for unpaid bills if they don't organise cut-off and payment themselves when they leave.
I also agree that it sounds as though the LL has misunderstood the request.
I have dreamed in my life, dreams that have stayed with me ever after, and changed my ideas; they have gone through and through me, like wine through water, and altered the colour of my mind. Emily Bronte