Technically, that's not true. It could easily be simply a matter of the accounts being incomplete or only some of them being wrong, not necessarily that they're all wrong. I do agree that the Bible is fiction and these accounts are not trustworthy narratives, but I felt the need to point out that your statement does not logically follow.
Other than that, I agree with what you've written. I mainly wanted to add an interesting twist to this:
An agnostic friend of mine is really into the writings of Bishop John Shelby Spong and has shared some of his writings with me. Although I don't care for the religious side of Spong's writings, when it comes to putting Bible stories in their historical context, he often raises interesting points.
One of the Spong newsletters that my friend gave me is called "Examining the Story of the Cross; Part 2: Did the Crucifixion of Jesus Occur at Passover?" In it he argues that the crucifixion wasn't originally connected to the Passover. The story was from later in the year but moved to the time of the Passover for liturgical reasons. In the middle of that newsletter there is a paragraph that includes discussion about the cursing of the fig tree. Here it is:
So, in addition to the fact that the versions of the story in Matthew and Mark are contradictory, the silliness of cursing the fig tree for not bearing fruit out of season may be an unintended consequence of restructuring the stories for theological reasons. That's certainly interesting to think about.