Confused about comparison of Pearson coefficients I am slightly confused on a paper I am reading. They have a table of calculated Pearson coefficients as shown here:
$$
\begin{array}
 . & I & II & III\\
A + B & 0.8 & 0.65 & 0.90\\
A + C & 0.73 & 0.46 & 0.83\\
B + C & 0.61 & 0.76 & 0.68\\
\end{array}
$$
They claim that the weakest correlation recorded was between $B+C, \,\, I$ and $B+C, \,\, III$. $A,B,C$ are different imaging modalities.
Are they stating that these are the two closest values in one comparison (i.e $B+C$)?
I am confused because they are now correlating correlations!
I thought the the weakest correlations would be $B+C, \,\, I$ and $A+C, \,\, II$, as they have the smallest values, but perhaps I did not understand their statement.
The paper can be found here: http://online.medphys.org/resource/1/mphya6/v40/i4/p041707_s1?bypassSSO=1
Page 4, section III.B
 A: The presence of errors in the values makes it hard to say much of anything because their comments may be based on numbers other than the ones either of us are looking at. Maybe they made yet another table between the original figures and the published table and their comments refer to that - if they are so careless, how could we tell what else may have happened? You'd need to ask the authors. 

would their statement be correct? Is it correct to say that if two correlations are close in value (within a given group) that they have a weak correlation? As in the table above, the smallest difference between two correlations is 0.61-0.69 as they state? 

The comment about weak correlation would presumably be because the correlation values themselves aren't large; you can't pick two correlations that are similar in size and thereby claim that the correlations are themselves correlated. 
There may be an argument that some of the correlations are in turn correlated, but an argument based on their values doesn't establish that.
