The Issue with Hebrew National is the brand had such a bad repution , it could not be fixed. Hebrew National is actually owned by a big food conglomarate who wanted to own “Premium brand” foods. After the purchased Hebrew National they found out most kosher keeping jews didnt eat it. They did reseach why and found it the supervision wasnt up to their standards, The research also said the OU was an acceptable supervision (Companies arent stupid) they then went to the OU to get the OU and the OU told them Hebrew national’s reputation was so bad they felt it could not be fixed and would damage the OU’s repution and so they refused to supervise it.
As a side note for many years Coke had a rabbi, when he died they did not want to tell anyone else the Secret Formula and the OU wanted more of a hint, They then went to the Triangle-K and supervised it for a while. Rumor had it Coke wasnt kosher, but most people just kept using it. Eventually the OU and Coke came to an agreement rearding the secret Formula