The video of Judy being the only one to save V is.... well, its over romanticized, with flawed logic.
Judy can tear apart old robotic tech and rebuild the tech with ease, yes. But The BioChip is not robotic, also with the prefix "Bio" there is an organic component to the chips matrix, and being a Prototype, very new and exclusive technology. It would be nothing like anything she as seen ever in her life.
Also, he was dead wrong with Johnny psyche being downloaded on the BioChip. It was not, the chip was not even around then. His psyche was downloaded to the "Soul Prison". Then 50 some odd years later for some unknown and very strange reason, he was placed on the BioChip. Plus, there is an unknown effect from the damage the chip underwent before Jackie slotted it in his port, and later into V's. The chip would of been around 80% integrity give or take.
Judy wanting to fix situations around her is more from her being an emotional train wreck. Classic running away from her own issues to fix others around her. Miako and Johnny at different times called it out....
... and that is from the first 4 minutes of that video.
If V can be saved I think it is from a barely mention Corp. (not sure who) It is mentioned in the news, there is a breakthrough tech for MS. As the article mentions MS can not be supplanted with implants, but this Corp has created nanites that can repair the spinal cord, using the persons dna. All one needs is $700000
The body attacking the brain, is something that can happen now, in real life, and can be treated. "Brain on Fire" book and movie based on real life brings it to light.