Because the thruster is an exotic perk not a subclass perk. Easy, simple, logical.
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Kepri sting granted invis to all hunter classes and its a class tree perk. Don't agree with op post either as shade step and blink would be something. I'm just stating that the logic of a class skill tree perk on exotics only work on that class vs normal exotic perks work on all is not true.
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I'm pretty sure the khepris sting thing was a bug.