If you EQ per song, then yes to an extent still. Though EQs have historically be designed to fix an audio system rather than to "fix" a song itself. Think about a normal speaker system. Depending on the room it may amplify and absorb different sound frequencies and at different locations. So if you change the location of the speaker system (IE install it elsewhere) you'll likely want to EQ said speaker system for the room that its in. This really doesn't change the recording of the song as it does change the sound of the speaker system. Normally one would EQ the speaker system to be flat, hence the entire equalizing name of it. Lately, this may not be true as people fix the speakers, or in this case, the headphones to their preference rather than EQing to individual songs or even genres.
If you want to look at EQing from the song's perspective, if you choose one EQ to rule them all (for that pair of headphones), then you're EQing all songs vs individual songs. You could argue that by EQing all songs you're changing all songs from their original "intent." However, each headphone on its own already colors the music hence you change the song's original "intent" by choosing a pair of headphones (or even a DAC/amp for that matter). Normally when we talk about deficiencies of music on Head-Fi using our descriptive words, each word will link to a certain instrument/set of instruments that aren't being reproduced properly. Hence the coloration or loss of information; loss of the original "intent" of the artist.
When I do headphone comparisons I will generally avoid EQing altogether though since 1) not everyone has access to an EQ and 2) that just adds a whole other slew of variables (what EQ do we choose, why do we choose that one, what happens if a headphone objective sounds better when it's not flattened to your preference?). If you begin choosing multiple EQs you run into combinatorial issues which just isn't worth it. The other thing that comes up is that EQing them could bring them further from the engineer's original intent and time spent; their intent if you may. All the time and effort they put into getting the headphones to sound the way they want it to and hearing that has gone away.
Tonality-wise, I actually still prefer the APP; it's a lot more linear to my ears. In terms of technical ability the APM is better.