A source can be partially true and partially false. One can start with a manuscript and point out which parts one thinks are accurate and which parts one thinks are inaccurate, without being "logically fallacious."
For what it's worth, I don't think there's enough evidence to prove conclusively that a real 1st century preacher wasn't the kernel of truth behind all the Jesus myths. There might have been one, or the stories might have all been fiction based on what was generally happening at the time, or at the time they were written down. I don't know if there's ever going to be enough evidence to know for sure.
But rejecting the Bible as evidence, when the question is "Was there a historical Jesus?" seems like rejecting the Sherlock Holmes stories when the question is "Was there a historical Sherlock Holmes?" It's the canon you have to start from, or else the question is meaningless. Without the Bible, we wouldn't even care whether there was an apocalyptic preacher circa 30 A.D. who had myths added to him.
There are several problems with the Jesus to Sherlock Holmes comparison:
First, we know that Sherlock Holmes was based on at least two real people: Joseph Bell and Sir Arthur Conan Doyle himself.
Second, thanks to the printing press the time Sherlock Holmes was supposedly in practice (1888-1917) is far better recorded then could be hoped for the time of Jesus.
Finally, with Holmes there is "The Game" where people try to put Holmes' case in a historical framework and the results are all over the map.