In "Aner Clute," a poem from Edgar Lee Masters's Spoon River Anthology, what hypothetical story does she tell?

The story of Aner Clute is the story of a woman whose reputation came undone due to a few bad choices. Her choices became known, which led to social opprobrium and, ultimately, ostracism. The hypothesis posed by this poem is, What would happen if people, particularly women, were allowed to err without being marked for life by one error in judgment? 
Aner's life is marked by simultaneous redundancy and instability:

Over and over they used to ask me,
While buying the wine or the beer,
In Peoria first, and later in Chicago,
Denver, Frisco, New York, wherever I lived. . .

Her buying of wine and beer is an allusion to her association with leisure. She started in a small town (Peoria), then goes on to larger cities, moving from one to another. The tone of the poem conveys world weariness because her use of the indefinite pronoun "wherever" expresses no attachment to any of these cities.
Everyone wonders "how [she] happened to lead the life, / And what was the start of it." They take a voyeuristic interest in her transgression, but no interest in her specifically, only the "start of it." 
She tells us how she explained her behavior.

Well, I told them a silk dress,
And a promise of marriage from a rich man--
(It was Lucius Atherton).

Lucius's poem directly succeeds Aner's in the anthology. His is the story of a vain playboy—a man who relied on his money and looks, though mostly his looks, to curry favor. He becomes a sad joke in old age. Unlike Aner, Lucius's flaw was not bad judgment, but a lack of self-awareness and wisdom.
She told others what they wanted to hear: that she was a woman easily fooled. She tells us, though, "that was not really it at all." She provides an allegory to explain what went wrong for her:

Suppose a boy steals an apple
From the tray at the grocery store,
And they begin to call him a thief,
The editor, minister, judge, and all the people—
"A thief," "a thief," "a thief," wherever he goes.
And he can't get work, and he can't get bread
Without stealing it, why the boy will steal.
It's the way the people regard the theft of the apple
That makes the boy what he is.

From Aner's telling, it is unclear whether or not she is an actual prostitute. She is clearly a woman who lives off of men. She embraced this lifestyle and its accompanying reputation because she could not escape it. She could not find work doing anything else because people would not allow her to do anything else, just like the boy who steals the apple in her story. Instead of lashing out and blaming her community for what she became, she allows them their myth of the "fallen woman." Their distant and disapproving regard for her, and whatever they believe her life to be, makes them feel good and righteous in comparison. This was her gift to Spoon River, and her burden.