An important point I should may be stress, though it may be obvious to some: There is grammaticality and there is naturalness and often people (in particular native speakers, not just of Japanese, but of any language) confuse the two.
Grammaticality means the sentence complies with the basic rules of the language. You can judge grammaticality by the sentence alone. To a native speaker, sentences that are ungrammatical will feel deeply wrong and confusing, often to the point of being nonsensical. However sentences that ARE grammatical can still lack any sense of meaning and be completely absurd (Chomsky’s “colorless green ideas sleep furiously” comes to mind).
Naturalness on the other hand depends HIGHLY on context and also on things like pronunciation/stress patterns/etc.
Textbook answers are often perfectly grammatical but highly unnatural (frequently to the amusement of native speakers), often because they contain too much information:
“Who is the girl in the picture on the wall?” “The girl in the picture on the wall is Mary.” (A natural answer would be something like “Mary” or maybe “Oh, that’s Mary.” etc.)
But in a different context, an unnatural answer may suddenly become perfectly natural.
A: (Looks at picture) “Who is the girl in these pictures?”
B: “Well, the girl in the picture on the wall is Mary, but the girl in the picture on my desk is Sue.”
(Here the extra information is natural because it’s needed to make the contrast)
This point is really important when it comes to wa and ga. For example, consider the four sentences from the start of Kuno’s exposition:
(1) a. John wa gakusei desu.
b. John ga gakusei desu.
(2) a. Ame wa hutte imasu ga…
b. Ame ga hutte imasu.
In (1), it depends entirely on context which one is more natural and appropriate.
In (2), “ga” is used in the plain statement, but in a contrastive statement “wa” can become appropriate as a contrast marker.
When you want to judge naturalness (in your own native language or in another), you HAVE to imagine a scenario where people might say the sentence and you have to imagine them actually saying it in the appropriate stress pattern.
(In writing, you have to consider what might come before and what might come after it)
Similarly, always keep in mind that someone declaring something as wrong might not be considering in the context you were considering it.