Unfortunately, a growl cannot be trusted. Your dog is starting to show dominance tendencies and I think you are right to question it. This is a big dog and there is no question that it is time to take him to a training class and to speak to a trainer about this problem. It's likely that your dog needs some specialized training for this specific problem.
In the meantime, it's a good idea to start leadership training in your home, but don't let this subsitute for the advice above. This is just a few things you can start until to get into a class or meet with a trainer. Do these things to assert your leadership:
#1. Implement the Nothing in Life is Free program. This means that your dog gets nothing, unless he does something for it, like sitting first, doing a trick, giving a paw, lying down, etc. Use this anytime he wants something including meals, snacks, outside time, rides in the care, etc.
#2. Always eat meals before your dog
#3. When going through a doorway together, the human always goes first.
#4. When playing with your dog, make sure that you stop the game, which means you will stop while your dog is still having fun.
#5. If you find your dog in the way of an exit or entrance, no matter where he is, make him move. Do not step over him.
#6.Help your dog roll over for a daily belly-rub.
#7. If your dog knows the "down" command, have him hold one 30-minute down-stay per day. No, that is not too long. It's ok if he falls asleep. Just make sure that you release him from the stay.
Lastly, do all the above things with confidence and kindness. Dogs always want to know who the leader is. They are much happier when they know this. In your house, the humans are boss. Hopefully your dog will learn this lesson easily and quickly.