more on Cortez and enthusiasm in August 1852

That allusion to Cortez (Hernán Cortés) and conspiracy in the August 1852 installment of Scenes Beyond the Western Border probably refers to the 1521 assassination plot led by Antonio de Villafana. Many versions of the story exist, in poetry as well as prose, including a volume of Uncle Philip's Conversations.  According to William Robertson, Cortes learned of the plot and

repaired instantly to Villefagna's [Robertson's spelling] quarters, accompanied by some of his most trusty officers. The astonishment and confusion of the man at this unexpected visit anticipated the confession of his guilt. Cortes, while his attendants seized the traitor, snatched from his bosom a paper, containing the association, signed by the conspirators. Impatient to know how far the infection extended, he retired to read it, and found there names which filled him with surprise and sorrow. But aware how dangerous a strict scrutiny might prove at such a juncture, he confined his judicial inquiries to Villefagna alone. As the proofs of his guilt were manifest, he was condemned after a short trial, and next morning he was seen hanging before the door of the house in which he had lodged. Cortes called his troops together, and having explained to them the atrocious purpose of the conspirators, as well as the justice of the punishment inflicted on Villefagna, he added, with an appearance of satisfaction, that he was entirely ignorant with respect to all the circumstances of this dark transaction, as the traitor, when arrested, had suddenly torn and swallowed a paper which probably contained an account of it, and under the severest tortures possessed such constancy as to conceal the names of his accomplices. This artful declaration restored tranquility to many a breast that was throbbing, while he spoke, with consciousness of guilt and dread of detection; and by this prudent moderation, Cortes had the advantage of having discovered, and of being able to observe such of his followers as were disaffected; while they, flattering themselves that their past crime was unknown, endeavoured to avert any suspicion of it by redoubling their activity and zeal in his service.  (William Robertson)

Some accounts emphasize that Cortés only pretended that Villafana had swallowed the paper naming the conspirators. According to Prescott, Villafana actually did attempt to swallow the paper.

A review of Prescott in the Southern Quarterly Review reports that Cortés "destroyed the scroll" without stating how:

He destroyed the scroll, and contented himself with the execution of the one ringleader. The conspirators trembled, but without cause. The magnanimous judgment of Cortes forbore farther inquiry. In an address to his troops, he told them that the guilty man had made no confession. His admirable policy never once suffered them to suppose that he had any suspicion of the guilty parties

Other sources likewise credit the actions of Cortés as great "policy." One biography refers to the ingested paper ruse as a "master stroke of policy,"  again the word used in the 1852 dialogue of C. and F. 

So far I have not found any report saying that Cortés burned the evidence of conspiracy, unread.

Possibly the reference in Scenes Beyond the Western Border merges two averted rebellions from the history of Cortes and the Spanish conquest of Mexico. First confronted with conspiracy, Cortés famously destroyed his fleet at Veracruz to prevent discontented men from deserting to Cuba. Legend has it that Cortés burned his ships. Even now "burn the ships" or something to the effect of burning your boats is a proverb of business success and life wisdom.  Nit-pickers insist Cortes scuttled his ships but did not actually set fire to them:

There is a popular misconception that Cortés burned the ships instead of scuttling them. This may have come from a mistranslation of the version of the story written in Latin.  (New World Encyclopedia)

Here again is the 1852 text as first printed in the Southern Literary Messenger:

F. " At last you have struck a chord that answers as to the touch of truth! And as for love, I know none better than that of the she-bear for her cub; and that lasts, and is returned, just so long as circumstance and interest bind."

C. "O! my friend! Is there not then a pure soul-love, a deathless friendship, "passing the love of women," which all life's trials and the world's baseness cannot soil or sap? If that be truth, 'twere better never to look into her Medusa face! O! better to cherish enthusiasm, (despite the sneers and ridicule of cold, calculating woman;) better, (as it would become) a blind heroism of credulity! Ay, a heroism of policy, —like that of the great Cortez, who burnt, unread, the proofs of a conspiracy, rather than embrace damning doubt."
(Scenes Beyond the Western Border, August 1852); and with significant revisions in Scenes and Adventures in the Army)

1857 book version:

"If that were truth, better never to look into her Medusa face; better to cherish illusion: blind credulity would be heroism! ay,—and policy,—like that of the great Cortez, who burnt the proofs of a conspiracy, rather than foster damning doubt."