If they told you it was fine, I wouldn't worry about it, but just to be safe, you might want to get him a passport. As a minor, you would have to take him to a passport acceptance place, and when you do, you will have to prove your relationship to the child. My DH and I will have to take my kids together, but if he couldn't make it, I would have to have a notarized letter indicating that getting passports for the kids was alright by him. As a single parent, if I am reading the passport website correctly, you would have a show proof of sole custody, like a certified birth certificate with only your name on it (and you have that, right?). You may want to check the passport website (I don't have the address handy, but I typed "u.s. passport" into a search engine, and found it easily).
I know that the rules for getting passports for kids has been tightened up because of the fear of people leaving the country with the kids due to custody issues, so if the passport official would take the application, and a passport is issued, I doubt
DCL would refuse boarding.
Have fun!
P.S. It takes at least 6 weeks to get the passport, so if you want to go this route, and you are going in September, you may want to do it soon!