I assume that since you work in an office at least 1/2 time your sons are in some sort of daycare or have a sitter. Do you know how incidents like this are managed in your absence? It might be worthwhile to talk with your child's caregiver. Some of his behavior may be a result of their expectations or actions.
Kids are going to get bumps and bruises, and you won't always be there. If he can self-soothe, that is a good thing. Just let him know that if he needs you, you are there. Offer to let him help you find a band aid or put together and ice pack if he wants/needs it. Tell him that you are sorry he got hurt. Let him lead the way in what he needs. He may not want to be fussed over, but you say he doesn't want you to walk away either. Calmly talk with him. Uh, Oh. That looked like it hurt. Do you need an ice pack or a band aid? Or, I bet you didn't see that tree root. It was really big. That's what tripped you. I wonder how old that tree is. I bet is has squirrels living in it. Want to look up and see if we can see any? Use the opportunity to connect in a way other than simply kissing away the pain. You might be surprised how wonderful that can be.