You can read their paper here[0]. I agree it's very dodgy (and without even looking at that author's past). While the comet 3I/ATLAS approaches within 53 million km of Jupiter (0.3 au), all they can propose is, optimistically, to bring Juno to within half that distance–27 million km. Hardly seems worth the risks? And that'd end all of Juno's remaining Jupiter science (assuming the MAGA! FY26 budget doesn't get to it first. It's fully defunded, if anyone hadn't heard).

Referring to their figs. 3–7, that distance figure is a hard limit—there's no possibility they have of getting closer to the comet than that.

(Keep in mind this is just one random interstellar comet; there are many, many others like it—there will be infinite opportunities to study one—and Avi Loeb is a proven clown who consistently misrepresents these things for drama).

[0] https://arxiv.org/abs/2507.21402 ("Intercepting 3I/ATLAS at Closest Approach to Jupiter with the Juno spacecraft")

Tangential remark: there was a similar proposal for the end-of-life of the Cassini orbiter—it didn't happen, but, there was enough delta-v for the theoretical option, of escaping Saturn and redirecting it to a second mission at Uranus[1]. It was also a dodgy idea, since the transfer time would have been ridiculous (~20 years)—it'd have been a long-shot for Cassini to have survived that long.

[1] https://en.wikipedia.org/wiki/Cassini_retirement#End_of_miss... ("Cassini retirement#End of mission options")