The reasons are just as you have read. You get multiple stems. If you don't pinch you get one or few stems. Despite the lovely flowers the sweet pea plant itself is a scrawny beast and in a garden situation looks better for having more stems. For exhibition purposes only one stem is allowed to grow so all energy goes into a reduced number of blooms.

sounds like the rule is consistent with pinching back anything .. in other words.. its not a special rule for vines ....

i will add the usual .. if you have more than one ... leave one or two unpinched ... and compare over the season ... and learn by experience ... i find i remember my own experiences better than things i read ...

ken