Deutero, the tension force of the brick angle pulling on the web of the header may cause too much deformation locally on the web or overstress the web out-of-plane. It won't happen in every case because it depends on the load, of course, and the size of the header to determine just where that brick angle connects. It was indeed complicated but in my case I had a very high load, long span and thus a tall header, and the header alone had to support the gravity as well as wind load. The angle did not bear on anything (horizontal expansion joints as you go up the building side). Vertical stiffeners may be small sections of stud or track or something else as long as it meets with the code requirements for vertical stiffeners. A continuous angle may serve for a horizontal stiffener when properly designed.
The angle bearing on each side wouldn't necessarily eliminate torsion because the support angle will still deflect even if it is sized to resist the entire load. A single angle will twist as well as undergo translation. Where it is fastened to the header, it will pull on the header. Depending on the actual detail you have, the header may have to resist some torsion due to the forced deformation the angle imposes on it.
I've used multiple nested studs and track for overly large headers. Others cases have worked out better with bracing to support headers for wind.