Where Did This Mistake Start?
The earliest instance I have been able to find of this misattribution is from the 1977 The Factory girls : a collection of writings on life and struggles in the New England factories of the 1840's edited by Philip S. Foner.
A transcription of the text appears in Part 4 "Three Pioneer Women Labor Leaders" in Sarah Bagley's section. Though Foner lists the September 18, 1845 edition of The Voice as the source, the quote is attributed to "S.G.B.," which does not appear in the original source, and contains some baffling alterations.
Foner appears to have started the selection from what would, theoretically, be the top of the paragraph. His version reads:
"Whenever I raise the point that it is immoral to shut us up in a close room twelve hours a day in the most monotonous and tedious of employment, I am told that we have come to the mills voluntarily and we can leave when we will. Voluntary! Let us look a little at this remarkable form of human freedom."
The opening of this paragraph in the original is much different:
"Mr. Miles somehow forgetting this old maxim [the golden rule], seems to suppose that a reasonable degree of justice to man is realized when the laborer is shut up in a close room from ten to twelve house a day in the most monotonous and tedious of employments. This is not wrong, we shall be told; they come voluntarily and leave when they will. Voluntary! we might reply, much the worse if they do; but let us look a little at this remarkable form of human freedom."
Barring the typical alternation (or exclusion of pronouns as in the last sentence), the selection continues like the original. These changes are necessary to establishing Bagley as the author - why, for instance, would she refer to operatives as "they" if she includes herself in their number - and disguise the original purpose of the article as a book review.
Unfortunately, there is no indication why these changes were made for The Factory Girls or where the erroneous transcription may have originated.
Pages 160-161 of The Factory Girls containing the earliest identified alteration and misattribution.