To avoid misunderstanding: the human condition is not the | same as human nature, and the sum total of human activities and capabilities which correspond to the human condition does not constitute anything like human nature (pp. 9-10).
No, H Arendt is not speaking out of both sides of her mouth. Instead she is disclosing her Kantian moorings. Lodged firmly in Kantian soil, Arendt is perfectly comfortable writing, as she does, both of the conditions that impose and press upon human beings (and therein constitute their state of being conditioned; hence, the Human Condition); but also the fact that what is human about human being cannot itself be conditioned without ceasing to be human.