Confusion between usages of linear RGB and sRGB
The monitor interprets its input data as encoded in sRGB color space. This means that to actually display them, i.e. to get brightness of the subpixels it does the transformation $C_{\mathrm{sRGB}}\to C_{\mathrm{linear}}$. This transformation is basically application of gamma of $\approx2.2$ to the value, so that output brightness will be superlinearly dependent on input data. Since non-extremal input values are $&lt;1$, they'll all be darker than with linear response.

Now if you have rendered an image in linear RGB color space, you need to compensate the transformation the monitor does. Thus you convert the image to sRGB, i.e. apply the $C_{\mathrm{linear}}\to C_{\mathrm{sRGB}}$ transformation. This transformation is inverse of what the monitor does: it applies a gamma of $\approx1/2.2$ to the values, so all non-extremal values will be larger than original.

In the OP I was coming to the wrong conclusion because of a mistake when trying to match the output of monitor with my input. To match it correctly one needs to either apply $C_{\mathrm{sRGB}}\to C_{\mathrm{linear}}$ transformation to input data to simulate what the monitor does with them, or apply backward transformation to the measured output — to undo monitor's processing.