I also think, that the "more than three hundred years" line shouldn´t be taken to literally.
What bothers me a lot more in this "revelation scene" is the explanation, that Voyager 6 supposedly entered a black hole. That would place a black hole in rather close proximity to our solar system, since it took Voyager 2 about 12 years to even reach Neptune and Voyager 6 must have reached the black hole within the ominous three hundred year time-span.
It gets even worse when you take a look at the section "Future of the Probe" at the bottom of this
article in Wikipedia - Voyager 2 has power for less than 50 years of operation. That would necessitate the black hole to be in VERY close proximity