Did you read the Nature article and look at figures 2 and 3? The trend is only down until the 19th century, then it's a steep upwards trend.
Sure did. You can pick several 100-year windows and see a similar upward trend. Long, sustained increase around 0. One similar to the one you reference around the year 600. Again, the TWO-THOUSAND-YEAR trend is downward, despite the several sharp-upticks along the way. The brief upticks are outweighed by the long drops.
As has been pointed out the window size used makes all the difference. For example, yesterday morning represented a 40 drop in temperature where I live. Oh noes! Global COOLING! That's compared to last week, though.
Are we aping our planet in pursuit of the American god named Profit? Yep. Should we be concerned about the dangers of coastal flooding? Yep. Does that justify the alarmist use of the hockey stick? Nope.