[glkindlmann]

Whether via direct or reflected light, spectra in trichromat's eyes are still projected down to a 3D space (the responses of the S, M, L cones). What you describe would still require a standardized and reliable way to probe an extra degree of freedom in spectra that conventional RGB displays can't access. The paper shared by varunneal explains it better than I can.

[carlosjobim]

If we assume that digital video/film recording will compress the spectrum to images which are composed of three colors, somewhere in the processes between the light hitting the camera and the light being emitted from a display to the viewer, that means any tetrachromatic person will notice a difference between the images and the real world.

[glkindlmann]

Sure, but noticing a difference between the images and the real world also happens with us trichromats too, e.g. colors online don't match those in the real world if the illuminant isn't correctly controlled. The intrinsic difficulty of color reproduction is not the same as detecting tetrachromacy. The nuance here is in generating stimuli that reliably and specifically detect the difference between projecting from an infinite-D space of spectra down to 3D (via metamers like the "keef" and "litz" described in the paper linked above), versus projecting down to 4D.