UGH Df doesn't have a copy of his lease and now he's afraid they won't give him a copy knowing full well I plan to move in. He's afraid they'll kick him out.
Kicking him out is one of the big points this procedure is set up to avoid. They need to be sure that immigrants will have a proper place to stay and not be thrown out of their accommodations because a lease was broken.
Underlying this is the public funds consideration. I.e., an immigrant on the streets invariably means public housing. So he'll need to do something.
OTOH, the fast-tracks are more relaxed about this aspect of the application as Vicky has pointed out, so perhaps a token effort will do.
And to the OP's comment about the courier deciding, the courier would know nothing more than the doorman at the consulate about the Housing Act of 1984 and it's relationship to immigration control. In fact, ironically, the doorman might be a better source.