The winning candidate has over 50% of the votes in the last round of counting.
So the winner under AV has the support of over half the people who voted in the final round.
AV doesn't magically make every constituent vote, it doesn't magically make a particular candidate win (or lose), it doesn't magically make all voters agree, in fact it isn't magical (in that way) at all.
People can argue over what a 'vote' is, what a 'preference' is, what a 'voter' is etc... but it seems to me that this is just campaigning tactics and nothing to do with the choice between AV and FPTP at all.
Under AV if you have given a preference to any of the candidates who have made it to the final round then that vote will be counted in that round, if you haven't then you haven't given anything to be counted!
When in conversation people may well say 'half the voters' or 'most of the constituents' or something like that, but while this is not precisely accurate I think you would be hard pressed to suggest that it is actually misleading (although some may try to make that claim!).
Under FPTP people talk about the winner having a 'majority' and talk of how large that 'majority' is... in fact, strictly, a majority means over 50% - not just more than runner up, but more than half the voters (or constituents). Under FPTP the winner actually has a 'plurality', almost certainly not a 'majority' or 'absolute majority' at all...
There is a huge difference between conversational use of words and attempts to mislead - some campaigners need to grow up a bit!
Here is an anti-AV video that deliberately tries to confuse 'over 50% support' issue and attempts to make it seem a deliberate lie - take a look, see what I mean - enjoy (or dont!). http://www.youtube.com/watch?v=X995SEN_QFs
I did leave a comment pointing out the error, but for some reason it hasn't been approved!