Yeah, what you are referring to, Ethan, is linear distortion but when people speak of distortion they usually mean nonlinear distortion.
A simple test to see whether an EQ adds distortion is to e.g. add a +5 dB boost followed by an identical -5 dB cut and compare the output to the input.
Software EQs usually operate in 32 or even 64 bit floating point numbers, so they achieve a higher signal-to-noise ratio than even perfectly recorded 24 bit files and extremely high dynamic range.
Some EQs, like Electri-Q, have an analoge mode that adds nonlinear distortion, but if you set it to digital it will be clean.
Last time I checked the iTunes EQ it was not exactly precise, that is a smooth curve in the user interface resulted in a jagged frequency response. You could call that unwanted linear distortion. Because of that, lowering all sliders but the ones you want to "boost" may result in something you'd not expect.
I never tried the simple test mentioned above, but could do so if you want.