Possibly a QGIS issue. You should report it on the QGIS issue tracker.
I've tried a couple of ArcInfo Binary Grids and QGIS reads them but won't access the attribute table. However, GDAL (which QGIS uses to read the grids) reads the table just fine...
$ gdalinfo test
Driver: AIG/Arc/Info Binary Grid
Files: test
test.aux.xml
test/w001001x.adf
test/hdr.adf
test/log
test/dblbnd.adf
test/w001001.adf
test/vat.adf
test/metadata.xml
test/sta.adf
Size is 250, 250
Coordinate System is `'
Origin = (0.000000000000000,250.000000000000000)
Pixel Size = (1.000000000000000,-1.000000000000000)
Corner Coordinates:
Upper Left ( 0.000, 250.000)
Lower Left ( 0.0000000, 0.0000000)
Upper Right ( 250.000, 250.000)
Lower Right ( 250.000, 0.000)
Center ( 125.000, 125.000)
Band 1 Block=256x16 Type=Byte, ColorInterp=Undefined
Description = test
Min=1.000 Max=1.000
NoData Value=255
<GDALRasterAttributeTable>
<FieldDefn index="0">
<Name>VALUE</Name>
<Type>0</Type>
<Usage>5</Usage>
</FieldDefn>
<FieldDefn index="1">
<Name>COUNT</Name>
<Type>0</Type>
<Usage>1</Usage>
</FieldDefn>
<Row index="0">
<F>1</F>
<F>62500</F>
</Row>
</GDALRasterAttributeTable>
