Oort objects are ill-behaved (erratic orbits). Inevitably some would wander off. Neighboring stars would have at least some Oort objects? Or we need to imagine a mechanism that prevents this.
Again, I think we're in violent agreement. The question wasn't whether they're likely to have some, it was more about how many and how far out, and more specifically whether it's likely to be feasible to hop from our Oort to e.g. Centauri's without having to traverse a huge void in between.
