The documentary suggested that the Somme was actually a veiled victory for the British after all. This was partly due to the effect of taking the strain off the French at Verdun as you both rightly mention, but also as a means of learning new tactics such as the moving artillery barrage and moving commanders nearer the front which had some measure of success towards the end.
This raises the question why did Passchendale prove such a disaster a year later? Interestingly the French alliance may have been partly responsible for this as well since the British were concerned about France agreeing terms with Germany. True the ground conditions were worse due to the mud, but the Germans also learned used new tactics such as retiring beyond the barrage, then firing on the infantry whilst trying to advance across the mud. Thy also learned how to interrupt infantry attacks by artillery and gas more effectively.
I'm all in favour of keeping dangerous weapons out of the hands of fools. Let's start with typewriters. Frank Lloyd Wright