IMO, either they're trying to hook a whale, or they don't want the work and are trying to scare you off.
Take the mechanic up on his offer. Coming on here and responding the way he has seems to show a lot of character and integrity, more than this frame shop seems to have. Try to get in there and help with it, you could learn a few things about working on vehicles. Even if you don;t want to work on them yourself in the future the knowledge and experience will do you good for dealing with other shops and mechanics in the future. He's not working anyway, so you aren't taking anything away from him, but be willing to work with him on time if a paying job come up.
--- Take the below with a grain of salt, these are the rambling of a tired man. I'm probably either not thinking clearly, not explaining it clearly, or both. ---
I'm still trying to figure out what they're talking about saying it's diamond shaped. I can only think of two damages on a frame thing that I'd consider a diamond.
First is the left and right frame rails being parallel, but not lined up. See the simple top down sketch of a frame below. (Yes, I know it's just a rectangle. I did day simple.

) Frame should be a rectangle like the top. Given the right hit, typically to front or rear corner, it might go kind of diamond shaped (technically a parallelogram) like the lower. If that was the problem, it isn't going to create a bow like the truck appears to have and would cause other issues like not driving straight. It's not going to be out that far though, think more like 1/4 to 1/2 inch and it could be pulled out. Frame shop could definitely fix this on a frame machine if it were the problem, often times it gets fixed by joe blow with a comealong and a pine tree in the back yard. If it were 5" out this way your bed would be touching the cab and you'd be driving sideways down the road, and there would be a bunch of other obvious issues that aren't there.
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Other thing I can think of would be that the frame was buckled from the side in which case the lips of the c-channel may have bent out (up and down), going from this shape [ to this shape ( if that makes sense. Viewed from the side that might give a diamond shape, lind of like this sketch. If that happened it might have cracked the lip of the frame and been welded back together. I suppose this could have resulted in the bow, but I'd still like to know where their 5" measurement is coming from. I wouldn't bother calling to ask though, I question if you would get an honest and/or understandable answer from them at this point.
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