If the 'account' of Peña is accepted, what, actually, did it say? The Handbook of Texas gives a brief summary.
"When Penñna's eyewitness account was placed together with other corroborating documents, Crockett's central part in the defense becomes clear. Travis had previously written that during the first bombardment Crockett was everywhere in the Alamo "animating the men to do their duty." Other reports told of the deadly fire of his rifle that killed five Mexican gunners in succession as they each attempted to fire a cannon bearing on the fort.... Peña reported that Crockett and five or six others were captured when the Mexican troops took the Alamo at about six o'clock that morning even though Santa Anna had ordered that no prisoners be taken. The general ordered their immediate execution; they were bayonetted and shot. Crockett's reputation and that of the others was not sullied by their capture. Their dignity and bravery was, in fact, underscored by Peña's recounting that "these unfortunates died without complaining and without humiliating themselves before their torturers."

Although there were many falsifications in the account, Richard Penn Smith's "Exploits..." of 1836 gave a similar account of Crockett's capture and execution. Many, however, wanted to have a more heroic death and told of his clubbing Mexican soldiers with his empty rifle and there was even one story about his survival to work as a slave in a Mexican salt mine.

See Dan Kilgore, 1978, "How Did Davy Die?," Texas A&M University Press, College Station, Texas, and J. W. Burke, 1984, "David Crockett," Austin Eakin Press.