New proof of cosmic inflation?

That is an epic logic fail. Other galaxies are 12 billion light years from us because the universe has been expanding in the intervening years. We are seeing those galaxies as they were 12 billion years ago, not where they were 12 billion years ago. Even though the expansion rate of the universe is accelerating it is nowhere near the speed of light and has not been since the Inflationary Period.
See How fast is the universe expanding?] on NASA’s site.