It was pretty much universally known as a forgery by scholars since the 1800s. It wasn't until the fairly recently that the idea that it was a mixture has bubbled up to the surface. But this camp is comprised mostly of christian apologists and theologians. The Josephus forgery has been well dismantled.
Arguing whether something is an "established fact" is a distraction since none of this isn't really falsifiable, all you can do is look at the evidence at hand. Here's a snippet from a 19th century book, Christian Mythology Unvieled, that outlines the argument:
"Mattathias, the father of Josephus, must have been a witness to the miracles which are said to have been performed by Jesus, and Josephus was born within two years after the crucifixion, yet in all the works he says nothing whatever about the life or death of Jesus Christ; as for the interpolated passage it is now universally acknowledged to be a forgery. The arguments of the 'Christian Ajax,' even Lardner himself, against it are these: 'It was never quoted by any of our Christian ancestors before Eusebius. It disturbs the narrative. The language is quite Christian. It is not quoted by Chrysostom, though he often refers to Josephus, and could not have omitted quoting it had it been then in the text. It is not quoted by Photius [9th century], though he has three articles concerning Josephus; and this author expressly states that this historian has not taken the least notice of Christ. Neither Justin Martyr, in his dialogue with Trypho the Jew; nor Clemens Alexandrinus, who made so many extracts from ancient authors; nor Origen against Celsus, have ever mentioned this testimony. But, on the contrary, in chap. 25th of the first book of that work, Origen openly affirms that Josephus, who had mentioned John the Baptist, did not acknowledge Christ. That this passage is a false fabrication is admitted by Ittigius, Blondel, Le Clerc, Vandale, Bishop Warburton, and Tanaquil Faber.'" (CMU, 47)
