Here is some of the discrepant output.   A1, A2, B1, B2 are the 4 
samples with tag counts.

My commands were
y=cbind(A1,B1,A2,B2)
d<- DGEList(data = y, group = c(1,2,1,2), lib.size = apply(y,2,sum))
alpha <- alpha.approxeb(d)
ms <- deDGE(d, alpha = alpha$alpha)

Here are the first 5 cases where both samples had Fisher's exact test 
p-values <.001 and the edgeR exact statistic >.05.  These
are raw p-values.


          A1            B1          A2         B2 
Sagenhaft p-value A1 vs B1       Sagenhaft p-value A1 vs B1        ms$exact
          46           5           39          12 
  7.546362e-11                          3.605042e-06 
       0.76524756
          33           4           45          13 
  1.128468e-07                          3.791248e-07 
       0.97325389
           0          55           13          49 
  1.070343e-15                          1.668152e-04 
       0.08834922
        69         179           92         526 
2.088333e-09                          3.816029e-55 
     0.56544378
     109          36          122          63 
3.988028e-12                          4.556175e-09 
     0.86574462



Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
University Park, PA 16802-2111

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