That's not true. Because the vote share was quite overwhelming remain, higher turnout will increase vote share for remain.

But the projected vote-share was calculated based on pre-ref poll data, and the port-ref poll as well. So if we are saying the early post-ref poll was wrong, the vote-share analysis must have been wrong too. Otherwise the final result would have been different, wouldn't it?

Analysts took the only two things we knew for certain - voting turn-out and total votes cast for each side, and used the opinion poll information to work back, and make the numbers fit. To do that, they looked at figures for each age demographic using "voting intentions" from the polls, as well as the post-ref poll saying how people actually voted and how it differed from the expected votes, and worked out the most likely demographic turnouts.

Changing any of the assumptions invalidates the conclusions, so we are left with the probability that the voting preferences for the demographics were not as previously thought. In other words, if more young people voted than previously thought, a lower percentage voted remain than thought, or the end result would have been different.