I interpreted Donjuanme’s comment as sarcastic, where “no way a background check would’ve stopped this” implied that they thought a background check wasn’t performed, but if it would’ve been, this murder wouldn’t have happened.
Not everyone who commits a violent crime with a gun has a previous record of doing that, or other indicators that would fail a background check for that matter. Not a lot of anti-gunners seem to remember that though, which is partly why I interpreted the comment that way.