"The gun was later returned to Santiago after he was released from a mental health facility in Anchorage".  It is not made clear whether he was actually "committed" and whether it was voluntary or involuntary.  If he was involuntarily committed, he would have had to petition to get his firearm returned.  This is how the law currently stands.  
This would change under the bill proposed by John Cornyn (R Texas), a person involuntarily committed could receive their firearms back upon release.
Background checks are not required at gun shows, private sales etc.  
If you are serious about preventing people with mental health issues from obtaining firearms, have mandatory background checks for all sales.  Period.  This the NRA opposes.
I'm all for increased care for the mentally ill, especially for our service men and woman suffering from the effects of PTSD, which is just as serious a physical wounds.  If it means more taxes, I'll pay it.