There are other ways to earn a Bronze Star besides the PH and CIB. For example, there are Bronze Stars with the Combat “V” and those without, giving an indication of general circumstances occasioning the award.
He had a badge from all three theaters (Europe, Pacific and Americas).
I think the he got the Bronze for stealing steaks from a Navy storage yard using a crane for a General’s meeting on Iwo/Guam. That’s the story he told us anyway.