I don't have any reason to doubt this account as an exceptional case of a deer running on pretty much pure adrenaline. The post mortem butchering does not lie: double lung and the top half of the heart damaged would be tough to misunderstand.
Last month I shot a jackrabbit with a BB goose load. This thing took a few pellets to the body and both hind feet were broken and hanging on by a thread, yet this jack took off and ran fast enough that I gave up trying to run him down (so I could put a 38 through his brain) and shot him again with the same load. Motivation can sometimes count for a lot.