Were they left by the last tenant, and hiding in the walls? 

J. beard not hiding at all. or expecting to have that from a pm. the mistakes have been plenty for example manager gave ok to tenant to move larger furniture in 7 days before lease starts. and they slept there, thinking they could 'move in'.

Extra addresses could be an attempt to hide something.

What benefit comes to me as a result of hiding myself from tenants?

looks like a place to hide a chest full of money..

All great insights already here Winn, but if you are able to oversee the painting, there are some ways to help with this often unavoidable turn over expense....For example, this time insist on some high end paint (think specialty paint store or the very best big box stuff); try a pearl or washable finish; I like one color for all the interior of all my units, ideally a white that can hide some imperfections (know and keep the code); this means no color or matching mystery later; then on the next turn over, see if you can't get away with just a wall cleaning; use a damp sponge mop with tsp or a tsp substitute  (and then rinse it with a clean water and a damp sponge mop)..not too much water, just damp.. 

Just because a tenant wants to pay upfront doesn't mean it's a scam or they're hiding something.

And now you are trying to police the tenants' use of who is using the washers/dryers.And if they're in-unit, you are now paying for the water for their relatives to come over and use their washers.And if you try to charge them an additional fee if they put in their own washers, they will try to hide them. 

Would you want to do a new property condition report when their furniture is possibly hiding damage?

Unless you are trying to hide the neighbors mess, I wouldn't install a fence.