How important is credit score when screening a young couple?

[Eric P.]

I'm looking to rent out my first place.  It's a nice house in an up and coming C neighborhood, so I'm not expecting perfect tenants.  

I met an engaged couple today in their mid twenties, I got a good feeling about them, very well spoken and sweet, familiar with the area.  Both work and have good work history.  They were very upfront that they're trying to build their credit.  Background came back spotless, both work and have a 3+ year history at the same places.  Their rent history shows no evictions, pay on time and no bankruptcy..  Problem is a very low credit score in the 480s with 4 different collections, these collections are all small amounts $150, $250, $400, $700.  It almost seems like these were simply accounts they forgot to pay as young twenty somethings do (I was guilty of this).  

If they check all the other boxes, how important is a credit score to you?