I don't get why this is so controversial.
For a lot of historical figures or happenings we know that the source material we have is unreliable. Take Pythagoras, for instance. As far as we know he didn't write anything. Neither did his followers, really, and we don't have good contemporary sources. Heraclitus and Xenophanes mentioned him, but not in any biographical detail, and in the case of Heraclitus it was an attack on Pythagoras which brings with it its own interprative problems. A lot of the later sources are stuff of legends, I assume a lot of people here have heard about the golden tigh. There are also a lot of fake writings attributed to him.
Despite of this few people doubt that Pythagoras was a real person, and most people believe that we have a reasonable idea of some facts about his life and some of his views on certain topics, though there are many disagreements about details and in some cases bigger disagreements about what is real and what is forgery or legend.
Surely Christians can have similar views about Jesus, God and the Holy Spirit, or Jesus/God/Holy Spirit if they're among the Christians who believes in the Trinity: That Jesus is real, that he is the Son of God, but that some of the source material - also things included in the Bible - is unreliable or untrue.
In fact, most atheists and agnostics have a similar view of Jesus as they do about Pythagoras. Namely that he was a real historical person who did stuff, but that the supernatural stuff is not true. That a lot of the writings about his life is either exaggerated, fakery or untrue, including most of or all of the Bible. I don't see why some Christians can't have a similar view, but that they accept more of the sources than an atheist or an agnostic would.
Add in that there's a long history of various Christian movements accepting stuff outside of the Bible as sources of knowledge about Jesus or God, like personal revelation, then a Christian, as in a person accepting Christ as the Son of God, has many potential paths to belief without necessarily having to accept the infallibility of the Bible.