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Wrong. They are not talking about rate of increase.
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That is correct. As I pointed out they are talking about a decrease because of how they cherry picked statistics. They picked an extreme value, 1998 (an el nino year and the second hottest year on record), as the starting point. If you throw out the outliers or start with more typical years the decreasing trend goes away and actually turns into an increase. You could use the same trick to argue that there's been a 50% decrease in temp since 1934 (the hottest year on record).
Imagine if you kept track of the local high temperatures for the week and they turn out to be 66, 68, 72, 95, 74, 76, 77. If you look at the trend from Sun. to Wed. it's increasing. The same is true if you look from Thur. to Sat. In fact it's true if you use the whole dataset. However, using the same data you can select Wed (95) as the starting point to show that the recent trend has been one of cooling. That's the same trick used when arguing that there is a recent cooling or stabilizing trend. If you start measuring before or after 1998 (assuming you don't pick another exceptional value) that trend disappears.
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Interesting, I'm trying to get my hands on the full article. I'm sure there will be criticisms over the next few months/years, but I really hope the study is correct and not another endless diversion and excuse for inaction if it's wrong.
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I've read the actual article myself and it's nothing earth shattering at all. About 2 years ago the same authors wrote a similar paper stating that globally the models predicted warming while the data showed a cooling trend. Turns out the error was in the observational data. After it was corrected and a longer time period was used the cooling trend disappeared. This time around they only address tropical temps rather than global and admit that the trend is warming, just not as fast as the models predict. The trouble is that the discrepancy is within the area of uncertainty so there is no way to say that it's even real. There are actually newly corrected versions of the observational data (which wasn't used in this paper) that puts the model and observations even closer together. There are numerous other papers on the subject, most of which conclude that there is a difference but we can't tell if it's real. This one only made big news because all three authors are very vocal skeptics and they sent out a sensational press release. Nothing in the paper shows that "Warming is naturally caused and shows no human influence" or supports the absolute statements made in the article.
As for Nahle, it's hard to dispute because I can't follow the point he's trying to make or how he's getting the numbers. I think he's trying to say that solar variability is closely tied to warming/cooling trends. That's never really been a question though. If that's his point and he concludes there is no anthropogenic impact, he's committing the fallacy of assuming a simple cause to a complex problem. Beyond that he's not an expert in the field so I certainly wouldn't count him as a credible source for original work. He may or may not be able to interpret existing data, but based on the conclusions he draws from the graph he provided I'd go with the latter. Either that or he's using different data.