History in the end is based in the records left behind by those who have come before. Sometimes the records left behind are deliberately falsified by those in history writing them. Always, the record is incomplete. Moreover, there is often records existing in such volumes that the historian needs to apply a filter to sift what is important to the aspect of the record that is the point of interest for him from that which is not.
To guard from the first type of error of falsification, the historian usually tries to balance the historical record left behind by one group with the record left behind by another. For example, for the record on Jesus, we have what the Gospel says. But we also have what Josephus says, and we have what certain Romans had to say. More than this, since the record itself has been handed down to us, and preserved through Christians, we often have additions to the record that are forged into the record to put a more positive Christian slant on it.
It is the job of the historian to draw a conclusion from that, to discern what in all likelihood has been forged, and to come up to a conclusion of who Jesus really was.
Professional historians train themselves to be dispassionate in the filters that they apply to the data, and the understandings that they derive from the texts left behind, but in truth, dispassionate analysis is something that is very difficult to achieve. Christians want to have their beliefs confirmed, but so do the atheists, for their very immortal souls depend upon them being right.
Truth itself is a passion for Christians also, and for most non-Christians too now, so in order to get the best idea of what the closest approximation of who the real historical Jesus is, we must critically read from all sources, and not just from the ones we would like to be true.
This is to say that without total freedom to present the facts as the individual historian sees them, without having different versions of history presented to us in textbooks as alternative possibilities, all history is fake. The historic question for example might be was the settlement of the American West a genocide? Without at least two alternatives being presented to the reader in the textbook, what is being presented is no longer history, but propaganda.
In our age, there is a plethora of different sources of information from a plethora of points of view. Historians present their points of view footnoted to the primary and secondary sources from which they have formulated their conclusions. I think in that kind of scenario, whether history is fake or not is very much dependant on the reader himself. It is really up to us to not just settle in to the story that is most supportive of our worldview, and to not just ignore any of the fact that are contrary to that worldview.
The bigger question is not whether or not history is fake, but whether or not we are going to be willing to settle for a fake history because it makes us feel better about believing the things that we do.