I start off my Lenten reading with chapter 5 of Dale Allison's Constructing Jesus, whose title is "Death and Memory." He sets up the chapter by acknowledging the issue that John Dominic Crossan decides in the negative. Crossan famously concludes that the biblical passion of Mark is "prophecy historicized" rather than "history remembered."
This question is old and the question is this. Did the earliest Christians make up the passion story out of prophetic proof texts? A large number of elements in the passion story correspond to phrases in the Old Testament. And just so we don't let ourselves off the hook too quickly, most of these are not predictions. In other words, we can't just make this an issue of whether one believes in prophecy or not. David flees to the Mount of Olives after learning he has been betrayed (2 Sam. 15). It is not a prophecy, but it is similar enough to what happens to Jesus for someone like Crossan to suggest that the whole Mt. of Olives part of the passion is made up to look like what happened to David.
Allison, whom I esteem as a straight shooter (which can make us uncomfortable, but we at least know he tries to follow the evidence wherever he thinks it leads), concludes with Mark Goodacre that Crossan's picture is too "either/or." Goodacre suggests instead that the passion is "history scripturalized," or as Allison puts it, "To biblicize is not necessarily to invent" (389).
Allison spends the next couple pages giving examples of Crossan's unjustified pessimism about Jesus' details.