There must have been a *lot* of talk if the studio PR folks felt the need to defend the issue so vigorously. By this point he’d been married and divorced once(about 2 years), and it looks like this article was followed up with a marriage to another woman (also about 2 years). It looks like his war service was a mix of real sea duty and war bond tours.
Looks like he had a daughter late in life. One bio claims a 1952 affair with Esther Williams, but that may have been publicity as well.
After the war, he had a series of longer marriages. So the record looks, at best, ambiguous.
Probably just a metro-sexual. Even today, they can come off as batting for the other team. Imagine that would look real suspicious in the 1940s.