You're absolutely right. Acknowledging your child's feelings, thoughts, and perceptions is essential. This will help him to trust himself over time, sharpening his ability to know himself and the world.
Denying the fact that he's hurt will also decrease the chances he'll come to you for help when he needs it. You want to set that good foundation when he's young so that when he's older, he knows he'll have good listeners in you as parents.
But your husband also has a good point. Nowadays, some parents overreact to the smallest little injury or problem, leaving our children to question whether they can handle life's complications.
So when your son takes a tumble, first, be open to finding out how he really is. If he really seems distressed, show him you can see that he is. Comfort and support are the best ways of moving past it. But if he really looks fine, tell them that he really does seem OK, and should be able to pop back up and continue on with his play. In this way, you'll help to build his resilience, which is an important goal for all of us as parents.