It is understandable that owners want to rush an application. They are anxious and excited to rent their property. They also need the money!
Don’t do it. Remember that you want a dedicated renter; someone who really wants to live there and is willing to wait. What you don’t want is someone who is fleeing from a bad situation or is desperate, or is so unstable that they can’t wait a couple days.
Take the time to get all the background information in. Take time to get to know the applicants and see how they react while waiting. It says a lot about someone.
Yes, there are times when we need to hurry but overall I like to take a relaxed approach and let the dust settle to see who the applicant really is.