I'm not sure why it's updating the video card's LUT. It looks like it's going for maximum colour accuracy at the expense of gray balance.
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Unfortunately I don't have a hardware calibratable monitor (yet ) but the only reason I can think of is that the Eizo calibration software updates the Videocards LUT to be sure it's linear, that means that it doesn't tweak the RGB values from the operating system/photoshop.
a LUT is nothing more then a translation table. It translates R,G,B, to R', G',B' were R',G', B' are corrected values for proper colour display.
Below an example from my current monitor profile (icc profile opened using MS Wordpad):
BEGIN_DATA
# ID R G B X Y Z
0 1 0 0 17.329 9.34629 0.927452
1 0.875 0 0 12.6458 6.8302 0.69593
2 0.75 0 0 8.80392 4.76363 0.505212
3 0.625 0 0 5.78843 3.14364 0.357655
4 0.5 0 0 3.51079 1.91771 0.246879
5 0.375 0 0 1.89861 1.0508 0.168689
6 0.25 0 0 0.84074 0.481617 0.118747
7 0.125 0 0 0.265462 0.172215 0.0912377
8 0 1 0 11.1763 23.8853 4.5426
9 0 0.875 0 8.33561 17.7644 3.36489
10 0 0.75 0 5.932 12.5979 2.37949
11 0 0.625 0 3.97122 8.39765 1.59463
12 0 0.5 0 2.44345 5.13725 0.992812
13 0 0.375 0 1.33741 2.77586 0.564622
14 0 0.25 0 0.601686 1.21134 0.283442
15 0 0.125 0 0.197463 0.353186 0.130257
16 0 0 1 6.89753 3.14656 36.0932
17 0 0 0.875 5.12829 2.35846 26.7932
18 0 0 0.75 3.63884 1.68712 18.9491
19 0 0 0.625 2.44373 1.14712 12.6574
20 0 0 0.5 1.51485 0.723885 7.7735
21 0 0 0.375 0.839167 0.417401 4.19966
22 0 0 0.25 0.387226 0.21016 1.81825
23 0 0 0.125 0.144998 0.0992423 0.53658
24 1 1 1 34.5609 35.6367 40.7166
25 0.875 0.875 0.875 25.7282 26.6057 30.4467
26 0.75 0.75 0.75 18.1335 18.8122 21.5683
27 0.625 0.625 0.625 12.0727 12.5571 14.4279
28 0.5 0.5 0.5 7.34231 7.64457 8.81315
29 0.375 0.375 0.375 3.96559 4.13023 4.76694
30 0.25 0.25 0.25 1.72005 1.78928 2.07344
31 0.125 0.125 0.125 0.491885 0.504968 0.598622
32 0 0 0 0.0602451 0.0612967 0.0806908
END_DATA
If a profile like above is loaded into the Videocards LUT, then it does affect the monitor. My profile is loaded by the Monaco Optix software that is executed from the "Windows->Startup" folder when my system starts up. When using a monitor that is hardware calibrated, there is no need to load anything into the Video cards LUT, except maybe a dummy profile to be sure the LUT is neutral. I am not sure but I expect that the Videcards LUT is reset, everytime you restart the system.
Maybe you should check if there is any calibrations software active other then Eizo's own software.