I was really just going to watch this thread and say nothing but decided to jump in and offer an opinion. I do so on the basis of having some personal experience with the gear in question. The qualifier is that I owned the 5D MkII, not the MkIII, so I can't speak to hands on experience with the new 5D.
I presently shoot with a 1D Mk IV and a 7D. I have also owned the 1D Mk IIn and MK III.
I have owned several copies of the 100-400 and gave them up because of less than optimum IQ at the long end. It was also a light hog and deadly slow. I presently shoot a number of 'L' lenses, including the 300 f/2.8L IS with both 1.4x III and 2x III extenders. I also shoot with a 400/5.6L.
It was mentioned that she could consider a 1D MK IV and 400/5.6L with a 1.4x extender. The AF speed is horrible and locking on the subject is chancy at best. I don't advise using that combo. For action, it would never work. It barely works for static subjects.
I find very little slowing of AF with the 1.4x on the 300/2.8 and the IQ is still excellent. On either of my bodies. The 2x really slows the AF down a lot... even on the 1D Mk IV and I use it only for static subjects. The IQ takes a hit as well, although not as bad with the MkIII extender as it did with the MkII.
Keep in mind that the 300/2.8 is not a light lens, but it performs like a champ. Mine will go into the grave with me. One of the best sports lenses ever made.
For what it's worth, the 7D AF is no slouch and the IQ is very good. The 7D is not up to the standards of my 1D MK IV, but it is still a serious camera. I can't compare it to the new 5D. I'm comfortable shooting the 7D up to around ISO800. Beyond that, I find it needs some work on noise reduction.
With a $10,000 budget, your friend can have the best of both worlds. She can have a 7D, 5D III and a really good used 300/2.8L IS with a 1.4x extender. A really nice, clean 300/2.8 can be bought used around $4,000. Don't waste the money on a 2x extender for action sports. It slows down AF too much for rapidly developing action.
Just my 2 cents worth.
After my original post, I felt I could have expanded a little on the AF capabilities of the 7D. If someone has used both the new 5DIII and the 7D for sports or action photography, they could offer a better comparison between those two cameras than I could.
Having said that, I normally use my 1D Mk IV for that type of shooting, but have had occasion to use the 7D in that application. I have used it to photograph birds in flight, Grand Prix auto racing and horse racing. It always performed extremely well and provided a high percentage of keepers.