In Oregon, an owner is allowed to charge a screening fee if they choose, to cover the costs of entire screening of applications. Ors 90.100.3 & 90.295
Of course, the owner does not have to charge... and have any method they choose as long as it is in keeping with Federal and State fair housing law.. and it is applied fairly to each person.
This of course is different than, first come first serve.. some folks use.
Consider,,, a smart owner does the checks... not just to protect thier property but to insure they are protecting the others or neighbors.
Also in Oregon.. the very act of renting... removes the possession of the property from the owner and 'awards' it to the resident... your home is your castle..
Would you let someone have control of your home or anything else without knowing who they really are, that they conduct themselves well?