Yes the article gives some caveats but it really isn't enough. C14 dating really, really isn't as simple as it looks. As an archaeological scientist (well I trained as one) the one thing that was drummed into our heads was that C14 cannot be accuratly used past 1950 and that C14 dating is a science based upon statistics and will never, ever give you one year as an answer.
The reason C14 can't be used past 1950 is that the whole thing is based upon the idea that in the past the amount of atmospheric C14 has always been the same as in 1950. We know this isn't true however. Since 1950 nuclear testing has really screwed with the amount of C14 in the atmosphere and we know that in the past C14 varied as we have ways of checking (this is mostly done by counting tree rings, I know high tech).
So we have adjust the results we get based upon what we know about the amount of C14 in the atmosphere. I'm going off track here so I'll just point you in the direction of a website that shows how C14 dates are calibrated. http://c14.arch.ox.ac.uk/embed.php?File=calibration.html#calibration
The main reason that this research is suspect is that C14 really isn't suited to this sort of fine detail work. I'm sure that you can date wine but the result you would get would be pointless. You could probably get a 95% certainty of the wine coming from a certain date range but that range would be so wide as to be of no use. If you want to get a precise date then you can but only by dropping your certainty to an amount to low to have any confidence in. Your magin for error would be astronomical.
I never thought I'd say it but who approves these non-articles to appear on