Oregon, has always allowedd a 'screening fee' and several years ago made a statute addressing the fee and process.
Owners are allowed to charge a screening fee if they choose, to cover the costs of screening of applications. Ors 90.100.3 & 90.295 this is the costs charged by the Credit bureaus and public information companies only.
App info; you need to provide documents to support the claims and facts you show on the app, it is not for the owner to 'prove' those claims or facts.
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 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?