Note that almost all the blue crosses lie below the green curve, and almost all above the red. The black line goes through the middle of them. Note again that this is not the best fit LCDM model, just a rough (0.3,0.7) so the actual fit is better than the black line. It may seem to the eye that there is not much difference, but this is real data we are talking about that have uncertainties. You have to consider that if the green line was the 'correct' model, what is the chance that almost all the data points happen to have been observed to lie below it, basically equivalent to say tossing 100 heads in a row. Anyway, that's a very rough way of putting it, using proper statistics you could quantify exactly what the odds would be, and they would be very low, hence this is a bad model.
The curve may seem close to each individual point but the key thing is that we must consider all points. If they all lie on one side of a curve that curve can't be a good model.
Edit: Oh and yes, newer data is important. Note that the curves separate more and more at high redshifts. Much of the new data is at a higher redshift than what I have shown, so make the differences between models more stark. This is particularly true for SSC since in that model there is only acceleration, wheares what we find is that SN above about z~1 show that the Universe was decelerating then, followed by the more recent acceleration. SSC doesn't predict this so would perform very poorly for the high redshift data.
Note also the SN are just one observation (although very important admittedly) and the other bits of evidence also suggest deceleration followed by acceleration.