Yes, it totally depends on the context. Grammatically, positive and negative are both possible for "noun (こと in your example) + じゃない(の)" (intonations are different in spoken conversations, though). As for "verb/adjective + じゃない(の)", じゃない(の) is a sentence final particle, and always works as positive (not negating the preceding word).
e.g.
選んだじゃない(の) = 選んだ
選んでなかったじゃない(の) = 選んでなかった
高いじゃない(の) = 高い
高くないじゃない(の) = 高くない
Incidentally, (人)が選んだことじゃないの! as "It was not their choice!" is often used in the context "It's my(or someone other than the mentioned person) choice!".