If Christians tampered with the Testimonium at all, why trust any of it? Once a passage is known to be doctored, shouldn’t the whole thing be thrown out?

That is a legitimate minority position, held by Ken Olson among others. The majority view among Jewish, Christian, and secular Josephus scholars is partial authenticity, for concrete reasons: the passage’s vocabulary and syntax are Josephan, and it sits naturally in a sequence of Pilate-era disturbances Josephus is otherwise narrating. The Arabic version once seemed to back this up, but Alice Whealey’s 2008 study showed it descends from a Syriac intermediary translating Eusebius, not from an independent line to Josephus, so it’s no longer treated as corroborating evidence. Textual criticism routinely separates a core from later accretions using internal evidence like this rather than discarding everything. And even if the Testimonium is set aside entirely, the crucifixion still rests on Tacitus, Paul, Mark, and the James passage in Antiquities 20.