Okham's razor dictates otherwise. A stronger probability automatically exists that Crockett went down swinging at mexicans as they stormed the walls simply because of the high frequency of this happening (it's how virtually everyone else in the fort died as well). The extreme complexity of the movie's version, by comparison, also diminishes its probability under the razor as it is contingent upon a succession of precise yet successively dubious events playing out in order, any one of which removed would alter that succession (1. Crockett survives the initial attack, 2. Crockett pulls back with a small group into the chapel, 3. Crockett survives the fighting in the chapel, 4. Crockett evades death at some location in the chapel for several hours until daylight, 5. Crockett is taken prisoner as the lone survivor, 6. Crockett is taken before Santa Anna where he is offered an unrecorded opportunity to have his life spared, 7. Crockett refuses that opportunity, 8. Crockett is ordered to be executed, 9. Crockett yells out an indisputably anachronistic late 20th century tagline, "I'm a screamer! Yeaaarggghhh!" as he is shot down).
Though the first two or three of these steps may have occurred, each successive one is more complex, more contingent upon the prior succession, and thus statistically less probable. By step 9 the statistical probability of it happening in light of the absence of any credible record that it did is virtually one in several million if even that, or otherwise negligible.
So no, non-seq, the new movie's account is NOT "just as possible" as the John Wayne/traditional account. It is only remotely possible, and as such substantially less possible, to the point of statistical negligence in the absence of credible and explicit records showing otherwise. It may be legitimately classified as (b) somewhere in between the other remotely "possible" though improbable death accounts of (a) succumbing to a sudden rapid case of Jim Bowie's illness in the final minutes of the battle and (c) being surrounded by invisible aliens on the verge of turning the battle's tide and getting bludgeoned to death by their light sabers.
The difference, of course, being that there are no written accounts of Crocket dying of typhoid, nor are there any written accounts of him being killed by invisible aliens. There are accounts of him being executed after the battle, and there are accounts of his dying during the battle. Since you weren't there then there is no way you can pronounce one version to be true and the other to be false. Unless, of course, the aliens told you.