I do not think this is true. The number of reports I have read where positions were abandoned after they had been flanked rather than having the defenders wounded or killed suggests that while shooting was important, it was less important than tactical manoeuvering.
"Win the firefight" was one of the basic elements of battle drill. The Germans organized their squads specifically so that the LMG would do the heavy lifting - and in the last year of the war, some squads had two LMGs. Imagine two MG42s going to work. The Germans expected firepower to win skirmishes for them. The "maneuvering" was usually done
before contact was made, as they emphasized infiltration.
So I do think skarper's comments have much merit, depending on the nationality. Some nationalities depended on cold steel and the shock of hand-to-hand combat, but that's not really 'maneuver' either.
The attack on the Brecourt Manor battery as depicted in Band of Brothers kind of gives a suggestion of how the Germans would have liked to do an assault. The attack force silently got close to the battery, set up their LMG, and then used heavy fire to bull their way further into the positions to achieve their objective. The maneuvering was done before contact was made, and after contact, they just headed straight down the communication trenches, using grenades and semi-automatic fire to keep pushing forward.