The archetype says:
Quote:
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Extra attacks from other sources, such as those granted by Manyshot or Rapid Shot, can be applied to only one of the wielded bows per round.
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So you are correct, with Rapid Shot turned on this PC should only have 3 attacks, not 4.
I suspect that these two bugs are the result of the archetype being so weird. Dual-wielding longbows? Totally gonzo.