Just had the same issue with our house. Bear in mind, this was my house and it maybe different for you.
In our case, the roof had had a past leak that had”sort of” been repaired. The water was pooling in the soffit at the garage and had soaked into the area above the garage door. This was causing the drooping like you have at your house.
Your inspector can’t see in there, so he’s really only guessing (as am I) from external indications and perhaps from what he can see from inside the attic.
I’ve been replacing fascia, soffits and siding anyway and on removal of the original siding, I had some rot in the outermost 2x12 requiring replacement along with part of the fascia and a small outer section of a rafter. (I dropped a few four letter words when I saw that the real problem had only been cosmetically fixed.) The trim board had drooped a little, but it was still okay and I just drove some 6” screws into it and leveled it for the time being. Maybe some day in the future, I’ll do a better job of it, but it’s fine for the time being.
Check your fascia and roof for indications of water penetration. You should be able to remove that lower trim 2x and replace it with a new one. You’ll get to see the condition of the headers then. It’s not a difficult job, but like everything else; time consuming and as with all renovations...be prepared for surprises.