Certainly untrue if respected contemporary historians, or scribes wrote down their history, and if they also were authors themselves.
Prove that Homer wrote the Illyad, or Sophocles wrote Oedipus Rex, or that any of Menander's plays actually exist (only one can be considered his and some small pieces from other plays). Prove that Julius Caesar actually wrote the Gallic Wars.
We depend upon traditions to set the "history" in place all the time.
The battle of Kadesh was considered for two centuries to be a great Egyptian victory, now we have good hard evidence to show that the Pharoah was just playing games to cover up a shocking loss to the Assyrians.
To use your "hearsay" legalist argument, hear say is quite sufficient to provide a "preponderance of evidence" in a civil case. it is not sufficient for a criminal case.
I also doubt that you understand what "hearsay" actually IS in a legal sense.
If I say George told me that Jack confessed to committing a crime, that is NOT hearsay evidence. Because I am there to be cross-examined about what George said.
If I testify that George told me that Sue said Jack confessed to a crime that is, in fact hearsay, because Sue is not there to be cross-examined.
So if Josephus says Christians told him about Christ's activities, then that isn't hearsay because Joseph witnessed what the witnesses of Christ record. If Josephus refers to correspondents who tell him what the witnesses to Christ said without attributing and identifying his correspondents, then that is "hearsay". However all this applies modern standards of journalism and law to times that were very different in their standards.
That is foolish in the extreme when dealing with history, and hagiography.
Do you know what hagiography is?
Regards,
Scott