I don't want to get into physics and optics
sorry but i do
the film does two things that affects what we see: transmit light straight forwards, and scatter light in a diffuse manner like how lcd monitor's antiglare
a clean film will scatter very little light, probably not a noticeable amount. in other words, if you shine a laser pointer through the film, you'll see a sharp dot on the other side.
now about its transmittance... this is the more important thing for us. IF the transmittance spectrum is such that the chromaticities of the primaries (i.e. the gamut) are unaffected, THEN the colors of a crt with and without the film will appear identical. once example of this would be if the film were a perfect neutral density filter.
now in practice, the film's transmittance spectrum probably isn't perfect and does affect the primaries. but does that matter? if the shift in the chromaticity of the primaries is small enough, yes there is still a shift but it doesn't matter at ALL. it doesn't matter if you want to call this an erroneous reading if the reading is off by an imperceptible amount
from my measurements, the differences in primaries between my g520p with film and my fw900 without does not appear to be significant, though i haven't plugged the numbers into a dE calculator yet. but regardless i don't believe it matters as whatever tiny difference between the primaries is quite a bit less than the difference of either monitor to any standard gamut (i think bt601 is the closest)
and no i dont have any "laboratory grade" instruments but that's not important because even my cheap dtp94 is precise enough to measure changes of under 1 dE. it doesn't matter if my 1 feet ruler is actually only 11.8 inches if i'm trying to see whether my left hand or right hand is longer.
if you can measure the difference between displays with and without the film, that's great, but if you just state that repeatedly without tell us quantitatively how much of a difference it makes, then it's completely meaningless information. if you measure my two hands and tell me that my right hand is longer, how am i supposed to interpret that? for all i know, it could be longer by half a millimeter, in which case its completely irrelevant, or longer by a centimeter