I got involved in a discussion about being able to put something back that you take out with EQ. I maintained that with good filters and careful setting, whatever you cut with one EQ can be restored by setting another EQ with the exact opposite settings. My counterpart in the discussion thought that even if you could come close it would be a phase nightmare. I decided not to get into the phase myth and carried on by saying that except for insertion losses (ie. the quality of the gear) there should be no difference. (Read this article though if you're interested in the phase thing.)
Mathematically it checks out. I'm not a smart enough monkey to go to all the trouble of working out the equations for the filters. But what I had at my disposal was a pair of EQs I could play with, match settings, and have no insertion loss. I dropped a track in my DAW and set up a real time analyzer plugin to have a fairly long sample time and took a screen shot at a marked point.
Then I dropped in an EQ with a 12 dB cut at 1 kHz, two octaves wide and took another screen shot. The trace you see in blue is with that filter in place.
All that remained was to add a second EQ down stream from the first and place a filter at 1 kHz with a 12 dB boost and see how the traces lined up.
The third trace is in white and you can see that it pretty closely matches up to the original. I even made it 50% transparent so you could see that there's only one tiny spot (at around 200) that's different. There's a slight difference in there because there was likely around 100 milliseconds of reaction time because I didn't have any way to automate my screen shots.
No phase issues. I rigged up a hot key to enable either both filters or neither, then closed my eyes and pressed it enough times that I wasn't sure which state things were in. When I pressed play and toggled back and forth I could hear no discernible difference in tonality. I even threw a phase meter on it and it didn't see any issues.
That got me to thinking why some people might run in to phase issues if they tried this in a venue, or even if they didn't, why they think they're getting phase issues from their EQs. I think the answer is in the settings and the quality of the gear. If you're using a twin third octave EQ on your main mix and you're not particularly careful about where you put the faders when you're setting things up, you could easily miss by a little. Even if you didn't, depending on the tolerances in the components you could still wind up with a bit of difference. Now anything that comes through the system in mono, like your lead vocals that are panned right up the middle, will be coming at you from two separate sources with slightly different responses. Phase issues.
So there you have it Brethren of the Knob and Fader. A real live myth of the audio world, busted right here with somewhat scientific practices for your edification.