We need some names, because that's the first time I have heard anyone say this.
I don't have a ton of experience with this, but here is some of the experience I had that made me think this is very possible. I do not know how to "scientifically" characterize this with the common graphs that people currently use to measure audio gear, this is all just subjective opinion. I also didn't try to extensively isolate for stuff such as room setup, etc. Obv the individual transducers, amps, wires, or whatever else you believe in will still sound different and I only tried to isolate out these factors in my head, I didn't go into any of this expecting to conduct a proper scientific experiment, etc.
Schiit Ygg A2 (mine) and Bricasti M3 (extended private loaner) - didn't sound better or worse on 2ch or headphones, but they had a noticibly different spatial presentation (ex: staging + layering) to me between 2ch and hp. A few other minor differences too.
All 3 of the below were in the same room with the same speakers and HP setup so those extraneous factors were probably drastically reduced. This experiment is what pushed me over the edge into holding my opinion about this:
Holo Spring1 (someone else's, but I heard the spring1 already a few times before this experience) - It was much easier to hear the flaws and shortcomings of the Spring on the speakers than HP setup. On the flip side, HP setup made the spring sound more slow and mushy and smoothed out vs speakers.
Holo May - sounded about the same, but "NOS sound" in NOS mode was much easier to hear on the HP setup vs the speaker setup. Speakers also sounded slightly more natural vs on HP the same tracks sounded more artificial.
Wavedream - sounded about the same with HP or speakers.
Aurender A10 (dealer demo) - sounded about the same with HP or speakers (again, only mentally isolating sound of different transducers, not scientific experiment).
Schiit Modi2, SDAC, and a few other inexpensive DACs frequently used in the hp world - sound great for the price on HP, didn't like the sound at all with any speaker setup.
Chord DAVE - similar result to above but at a much $ price point - tried on speakers once, didn't like it, but not bad at all on HP.
1 MSB, 1 Nagra, and 1 Technics DAC (I don't remember the model names as I had no intention of buying, the potential buyer was cool and had me go into the demo room with him during his demo) heard at a dealer - different price points (2 of which were on the high end), but all 3 were IMO overpriced for what you get on speakers, but still good absolutely speaking. When I tried the MSB with headphones, I didn't think it was good for the HP (my headphones and their amp). Staging and layering were all messed up relative to other more $$ DAC options talked about here that don't cost nearly as much as the MSB. I remember I didn't like the Technics with HP either but I don't remember what exactly I didn't like.
There are a few more examples I have, but point is as one person my experience has been that some DACs do sound better to me on either HP or speakers while others are about the same.