Opinions, opinions, we rely on others opinions so much. Grading is an opinion we all know that. So whose opinion do you trust?
Everyone here has seen coins in both company's holders that we disagreed with the grade. Both companies have graded counterfeits as genuine, both companies have graded genuine coins as counterfeits, so what to do?
I would start with a phone call to the first company to see if they would agree to a no cost second look. If they do not I would call the other to see if they would do the same. If not I would look to a third company or an industry accepted expert in the series. Is it moral to do nothing or sell them as is? I would say yes. The holder is the guaranty from the company, Is it immoral to sell a coin that NGC or PCGS graded MS 67 that you think is no more than MS65?
Grades are opinions of a certain grader or graders of a certain company at a certain time, so is the authenticity, nothing more.