There are many reasons why he would not have a purple heart. If his injury was not combat related or he did not feel he really deserved it - he may never have applied for it. Sometimes men felt that their wound was not worthy of recognition in comparison to a comrade that was blinded or lost a limb, etc.
Later on however, men found these medals were valueable as they raised the ASR score - the score listed on the bottom of WW2 discharges - the higher the points, the faster you got home.
The Bronze star could be awarded for non combat achievments - the inventor of the Cullen Hedge row device received one for example. A Bronze star for heroism would probably have a "V" device - and this would be noted on his discharge papers - along with the General Order number outlining why he received the award.
Since he received a VA pension the VA would have the specifics of his service related disability.