They may have invented the GPMG concept, but its usage in post-war armies differs markedly from the ways the Germans used it.
The machine gun was the focus of all small-scale infantry tactics – the German rifle squad revolved around it. It was their firepower, and the whole squad was devoted to its deployment, care, and feeding. In other armies, as George’s tract says, it was merely a support weapon.
GPMG is in the light role tend to be a bit heavy, and in the medium role tend to be a bit light. Indeed, the British re-chambered the Bren gun to 7.62 mm and kept using it until relatively recently as the section support weapon.
Many modern armies don’t use a GPMG at section/squad level any more – they often use a light support weapon. This is typically the standard rifle with a longer barrel and bipod. This is more akin to the BAR approach, and, like the BAR, is incapable of any really sustained fire, and makes a poor substitute for a light machine gun – hence the recent emergency adoption of the Minimi by the British Army to fill the gap. You will also note that the US adopted the Minimi as the Squad Automatic Weapon, after having previously adopted a GPMG which was intended to replace all other machine guns.
So no, the GPMG at squad/section level is by no means universal.
Edited to correct something