(I previously posted this as an answer to this question, but <PERSON> wanted to focus on actual textual analysis rather than discussing the intent issue, so I've separated this out into a new Q&A)
It's easy, even for people familiar with literary analysis, to conflate asking "Did the author mean this?" with "Does the work mean this?".
As you'd expect with an issue like this, there's no objectively true answer about who's correct here—asking if the author is right doesn't make a lot of sense, because there's no scale to measure right against. Instead, I'll introduce some of the common schools of thought on the issue of authorial intent (how you should interpret what the author wanted to say).
Author
Some people would argue that the author—the person who created and crafted the piece of literature—is the one who knows most intimately what they intended to convey through their work. This view was favoured by the majority of literature critics until around the 20th century, when New Criticism and the intentional fallacy became more accepted.
Biographical criticism is one of the schools of literature which favours the author's intent and meaning as opposed to examining the text alone:
Biographical criticism is a form of Literary criticism which analyzes a writer's biography to show the relationship between the author's life and their works of literature. Biographical criticism is often associated with Historical-Biographical criticism, a critical method that "sees a literary work chiefly, if not exclusively, as a reflection of its author's life and times".
This longstanding critical method dates back at least to the Renaissance period, and was employed extensively by <PERSON> in his Lives of the Poets (1779–81).
By using context of the author's life, views and experiences, biographical criticism tries to uncover meaning through what the author may have intended to convey. Historically, this tended to be applied rather literally—the author's word was taken to be generally true without debate. This is not necessarily true in more modern analysis, though, where a balance is achieved between accepting the author's word and the other factors.
Text
New Criticism is the form of literary criticism that comes to mind when considering the text as the primary source of meaning. New Criticism emphasises close reading (for context, see 'http://literature.stackexchange.com/questions/1885/what-is-close-reading'), and tries to find meaning through the author's choice of words rather than their experiences and historical context.
It is debated whether New Criticism's method of almost entirely excluding historical context is effective. In The New Criticism: Pro and Contra, <PERSON> outlines the major issues with New Criticism:
Four accusations are made more frequently. 460
First, the New Criticism is an "esoteric aestheticism," a revival of art for art's sake, uninterested in the human meaning, the social function and effect of literature. [...] Second, the New Criticism, we are told, is unhistorical. It isolates the work of art from its past and its context. Third, the New Criticism is supposed to aim at making criticism scientific, or at least "bringing literary study to a condition rivaling that of science" [...]. Finally the New Criticism is being dismissed as a mere pedagogical device, a version of the French explication de texte, useful at most for American college students who must learn to read and to read poetry in particular.
It is worth noting, for context, that <PERSON> was not criticising New Criticism himself—he was merely outlining the common flaws pointed out by others.
Reader
There is another prominent group of literature critics who eschew both of the above approaches, instead favouring you as the main decider of a piece's meaning—reader-response criticism.
What reader-response criticism tries to say is that a piece of work does not have one objective meaning that can be determined through careful analysis. The linked Wikipedia article phrases it well:
Reader-response theory recognizes the reader as an active agent who imparts "real existence" to the work and completes its meaning through interpretation. Reader-response criticism argues that literature should be viewed as a performing art in which each reader creates their own, possibly unique, text-related performance. It stands in total opposition to the theories of formalism and the New Criticism, in which the reader's role in re-creating literary works is ignored.
While writing this, I've reflected on the issue a little, and reader-response criticism starts to make a lot of sense. Critics in the past have read pieces and tried to find a way to interpret works and find meaning, as if it is an inherent property of a work, but, as shown by the many schools of literary criticism, each reader does find a different meaning. 460