Your textbook is wrong in saying that [2] is wrong. Whenever P and Q work in the opposite direction towards expectation of R, P ではないが Q is okay. For example, it is fine in the following context:
A: だれか、アジア人はいませんか。
'Is there any Asian?'
B: 僕は日本人です。
'I am a Japanese.'
C: 僕は日本人ではないが, シンガポール人です。
'I am not a Japanese, but am a Singaporean.'
In this context, 僕は日本人ではない closes up one possibility of C being an Asian, but then, シンガポール人です opens up another possibility, working towards the expectation of, and in fact affirming, C being an Asian.
Usually, you read as it is written. If you want じゃなく, you will usually write so. But it is not that wrong to read ではなく as じゃなく. It is wrong/correct to the extent that reading English cannot as can't is.
Actually, even when P and Q do not work in the opposite direction, you can use PがQ as long as P is providing a new topic into the discourse.
彼は試験に受かったが、これは普段からの努力の賜物だ。
'He passed the examination, and that is due to his consistent effort.'