This idea of an interpolated marginal note is Carrier's own contribution, first published in the peer-reviewed Journal of Early Christian Studies in 2012. While elegant, is not the only explanation. In his blog [1], Carrier references several recent publications (peer-reviewed, as he likes to emphasize), including one published in Journal of Early Christian History in 2017 by a South African historian Nicholas Peter Legh Allen, who argues that the James passage is a forgery, of which his prime suspect is Origen [2]. So, you can see that Carrier isn't the only one among modern academic historians of antiquity who casts doubt on Josephus passages.
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[0] Josephus and the Testimonia Flaviana in On the Historicity of Jesus, 2014, p. 332-342
[1] https://www.richardcarrier.info/archives/12071
[2] Abstract at https://www.tandfonline.com/doi/epdf/10.1080/2222582X.2017.1.... Full text can be found in: Christian Forgery in Jewish Antiquities: Josephus Interrupted, 2020, of which a pirated pdf exists online