tl;dr: Yup, the DT playback isn’t flat. But it is only a very subtle (≤1db) bump at 5kHz, and a more pronounced roll off above 12.5kHz.
I did some white noise spectrum analysis:
I generated a 30s white noise file. Here’s a spectrum analysis of it:
Then just to calibrate my set up, I played that out my audio interface and recorded it back in:
These are flat well within a db, so we can assume the set up is good.
Now I transferred the same white noise file to the DT. Set it on a default pattern, default track, adjusting only the amplitude to have infinite decay. Now, I played that back on the DT, and recorded it through the same interface, set the same:
There is slight 1 db roll off down from 5kHz, then flat until a gentle roll-off starting at 12.5kHz.
This tiny (≤1db) ramp down below 5kHz might account for what people are hearing. I imagine the high end (12.5kHz and above) roll off contributes more to the character of the DT sound.
Finally, to see if the recording side of the DT had any effect, I played the sample into the DT and recorded it there, then played it back into the test set up:
Pretty much the same, though you can see the effect of the essential sampling filter (at Nyquist) at the very high end. We can conclude that the sampling side of DT has no significant coloring.
Updated: I redid the DT transfer portion with a white noise sample generated at 48kHz.