Yes, it's a MOSFET input op-amp, so the bias current is not a factor.
I suspect it's more likely because it's a rail-to-rail op-amp, which actually has two input stages: one of voltages near the positive rail and another for voltages near the negative rail. As the common mode voltage varies, the op-amp will switch from one input stage to the other, possibly using both at the same time, at some point. The two input stages will have slightly different offset voltages, which would explain why it varies, as the common mode voltage is changed.