The public is asking the authorities to be more vigilant.    They can't do that without imposing the same rules/laws on both the innocent and the guilty.  If beating ones wife is a possible indicator of violent tendency, I would hope it would be a part of liscensing a weapon to be sold.  

Yet as you stated, with no conviction, you only have an accusation - not enough.*    But it could still be considered if the buyer also happens to have other indicators to go with that.
 
      *Many people do not bring charges in domestic violence.   You and I both know that.  That doesn't mean the violence didn't happen.

Tough call.