I like this question very much - many popular history of mathematics books seem filled with legends more than history.
I would expand the question "What are some good papers that debunk common myths...?" to include books as well as papers. Maybe the best books to debunk myths are books that directly discuss and include the primary source material (in translation, perhaps). A fantastic recent book in this spirit is "The Mathematics of Egypt, China, India, and Islam: A Sourcebook," edited by Victor J. Katz. This is a great value as well! For example, an scholarly translation of the Chinese "Nine Chapters on the Mathematical Art" costs around 350 dollars on Amazon -- but one can instead find it in this sourcebook, together with a multitude of other translated texts, for around 50 or 60 dollars.
To demonstrate that this book addresses your specific question, on pages 467-477 you can find a translation of the Bijaganita of Bhaskara II. At the end is Verse 129, the end of which is translated, "Hence, for the sake of brevity, the square-root of the sum of the squares of the arm and upright is the hypotenuse: thus it is demonstrated. And otherwise, when one has set down those parts of the figure there, [merely] seeing [it is sufficient].
The author of this section then mentions "These verses are presumably the ultimate source of the widespread legend that Bhaskara gave a proof of the Pythagorean theorem containing only the square figure shown in figure 4.19 and the word 'Behold!' "
The figure (4.19 in the book) is not among the verses in an old text, as far as I know. I think that Indian texts of the period were traditionally written on palm leaves (which degrade somewhat quickly), and copied every generation or two, so we don't have very old texts. In any case, the "Behold!" legend for the Pythagorean theorem seems to be a myth or at least a vigorous embellishment of history.