The "serious doubt" is based on the fact that one Greek manuscript, Sinaiticus, simply omits
Mark 16:9-20. One other, Vaticanus, also omits it, but leaves a blank space exactly the right size for the inclusion of the passage. This proves that the scribe copying the manuscript was either working from a more ancient manuscript that incuded the passage, but he for some reason ommited it, or that he was working from a more ancient manuscript which also ommited the passage, but which also left the blank space, indicating the testimony of a still more ancient manuscript. In any case, the blank space left by Vaticanus testifies to the existance of the passage prior to the copying of the manuscript, which is dated about 350 AD.
Every other manuscript extant which includes Mark includes the passage in question, as do the earliest church fathers, the most trustworthy ancient versions, and the lectionaries.
You Can Understand the Bible by Daniel L. Seagraves
eighth printing 2006, pgs 187, 188
ARPH