I think that this paper has an implicit assumption of conspiracies in the modern age, where failures of conspiracy could potentially be more widely circulated as technological progress makes it easier to communicate failures (It isn't part of those considerations that are stated in the paper, but I would say this would make a great topic for another paper!). I hypothesize that it would have been easier to keep a conspiracy two millennia ago, given that failures were probably less prone to dissemination. In addition, the communications technology of the time was paper (for those who were literate), and word of mouth, which relied on memory. This introduces 'noise' into communication of those failures, or indeed, distorts the truth of what did occur. Specific to your question, a conspiracy surrounding a hoax resurrection of Jesus would probably have gone on undetected.

Separately but related, you also have to consider confirmation bias and the tendency for people to cling to challenged beliefs in the face of contradictory evidence.

Bottom line: You'll just have to take Christ's resurrection on faith. ;-)

As far as we know in 2016, there are no direct "witnesses at the time". Scholars seem to agree that all the fonts about the events described in the gospels are (at least) second-hand accounts of oral traditions.