What is right?
There's no such thing as right or wrong in this hobby. You can only judge by the level of your own perceived enjoyment.
Every sound you'll ever hear will be processed thru your ears, which are not only different from others, but will change overtime as you age.
Why do you think the Harman curve is an average and a targeted frequency, and not an absolute value?
There's no absolute truth or a 'right way' to do things in this hobby.
It's whatever floats your boat.
I'm not one to buy into the whole, all ears are different. In a healthy range ears will hear the same thing but the difference is once experience which leads to perception. If one owns Grados then listens to say a DT770, they can perceive that has a smooth sound, it isn't it's smoother because what they're used to is a more extreme treble.
If you play an instrument, Piano, Guitar etc. Say a Fender from the last few years, full bodied, resonant, and a certain headphone doesn't capture that body then it's not within the range of having a correct timbre.
Neutral in a headphone doesn't have to be perfect, but it should be able to not interfer with the instrument or singers voice to the point it sounds unnatural. Warmer headphones tend to be more accurate in my experience, they're able to give you the resonance of wooden instruments, bass decays. Many planers like an Audeze phones for example lose out on that, which leads to them having a more plastic timbre rather than having the natural warmth due to the linear bass, mid bass is flatterned out and headphones need that mid bass to create the things I just mentioned.
If you have a reference, take a certain % for things like mic colouration, source gear you gotta have a personal target and the closer the more it gets a nod so to speak. Can this headphone reproduce the voice as intended, close to the original recording? Are all reverb, natural decay audible and does it add or take away, if so by how much? Some people use spectrum analysers, I have in the past, you do need a trained ear however too.
One thing a lot of people do is only having one or two phones and no reference. I have at least 10 phones around me here at home, some I bring from other properties, work etc. Not to swing my pole around but the reason I bring this up is I see it as a cleanse, I don't like getting used to a certain sound, you miss imperfections, one could argue if you get used to it what's wrong? I do it because it reminds me that what I hear is what I hear, if my HE-6 for example sound smoother, I've probably temporarily adjusted or I need to play a reference track in case the mastering is smoothed over.
before I bloody rambled your question was what is right?
My answer is the headphone that can consistency reproduce timbre, voice, extension, reverb, body as close as possible, more consistently.
When a headphone sounds way off on something you know doesn't sound that way then you have to make the argument it's wrong.