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My take on it is this: Russel has an idea, and the idea is that there's a world of sense-data and a "real" world supposedly hidden from us. This shows up in Kant also; it's essentially the phenomenon-noumenon distinction. Because of this, Russel says that the existence of the sense-data of a chair does not necessarily indicate the existence of a "real" chair, which supposedly underlies the sense-data chair (and may cause it, although such things would be impossible to show one way or another).
I take issue with the word "seems" here because it is the direct result of this idea of Russel's. Frankly, I can't make sense of what "sense-data" is supposed to be, even with Russel's explanations (and by that I mean that I don't see how it can be asserted meaningfully). Since that's the case, how could a skeptical doubt about the chair perhaps being a not-chair possibly arise? Grounds for doubting the chair's existence simply aren't there.