Hmmmm, that graph shows thermal "resistance" which is exact inverse of thermal conductivity. So, yeah, physics is never wrong (almost?)
EDIT: OK, it seems an explanation is due since that source appears to give contradictory information, while it's not. There is a misuse of terms on my part as well as that source.
To clarify, the thermal conductivity is measured with W/mK and it's the heat transfered per unit time over 1m2 area through a 1m thickness when the temperature differential between the surfaces is 1 K.
Actual heat transfer per unit time (e.g. Watts) depends on area and thickness, and it increases with area but decreases with thickness.
The source refers to m^2.K/W as "thermal resistance" but it's more correctly referred to as thermal insulance.
On the other hand, the reciprocal of thermal conducitvity is actually called thermal resistivity (mK/W), and it is different from thermal insulance and thermal resistance (K/W).
Basically, thermal resistance considers the area and thickness of the material, while thermal insulance considers only the thickness, whereas thermal resistivity considers neither.
As a result, a thicker (e.g. 3mm) material can have higher thermal insulance (m^2.K/W) AND have higher thermal conductivity (W/mK) at the same time, than a thinner material.
If you call thermal conductivity x and material thickness L, then thermal insulance is L/x, meaning thermal insulance increases with thickness.
Going back, it turns out I was wrong, the 3mm graphite pad does have higher thermal conductivity than a 1mm graphite pad, but at my defense I had thermal conductance in mind. Thermal conductance (inverse of thermal insulance) is the Watts through a particular thickness (when temp diff is 1K). In that respect, I was right too, because a 3mm graphite pad does carry lower Watts than a 1mm pad.
So, we were both right. Case closed
