I haven't personally seen purple loosestrife as a dominant plant in acid bogs. Occasionally I'll see it around the edge of a bog, presumably because the soil there is more neutral. The only invasive that I recall seeing in a bog (actually more of an acid swamp) was Lysimachia nummularia, or Creeping Jenny. Some of the native "loosestrifes" occur in bogs, like Lysimachia terrestris and Lysimachia thyrsiflora.

I can think of one acidic lake (rapidly turning into a peaty bog) that is completely infested with purple loosestrife.