Statistically significant with 95% confidence means that the probability that we would see data like those we have, in the case that there is no warming, is less than 5%. Now, if this level were 10%, we might say: Well, this data we are seeing could in fact just be a fluke -- we can't be sure. That's something entirely different from saying that data indicates there is no warming.
If you want to claim that there has been no significant warming, you would have to compute the probability that we would see similar data in the event that there is warming going on. This probability will likely be nowhere near as low as 5% or even 10%.
The end result is that while the data doesn't indicate there is warming with statistical significance (only almost), nor does it indicate that the temperature has remained flat, with any statistical significance. That is, the data for this particular period tells us nothing with certainty -- we simply have too little of it. But if anything, the data that we do have support the global warming hypothesis more than it supports the random variation hypothesis.
Trying to use this as an argument, not only against global warming, but against any precautions that even consider global warming a possibility, is frankly idiotic, especially considering all the other data that we have.