Various things will have an effect without changing FR.
Higher distortion won’t change FR. (Since even if you have high enough distortion to meaningfully alter the magnitude of the signal, it’s altered the same amount at all frequencies unless the THD vs freq is nonlinear.)
Crosstalk won’t affect FR since if measuring both channels at once, again the magnitude alteration will be constant. And if measuring just one channel crosstalk into the other channel has no effect anyway.
More dynamic changes that either only kick in or whose modifications are dependent on the content of the signal or the relationship between the signals in the left/right channels won’t necessarily alter FR either.
Again in music production there are huge varieties of tools like delay, reverb, M/S, compression that won’t directly affect FR. If FR was always the thing changing then EQ would be the only tool ever needed.
Even in situations where other factors are nonlinear vs frequency, so for example a device with way higher crosstalk at high frequencies which would mean that more of the signal from the right channel leaks into the left, thereby either superimposing and increasing amplitude at higher freqs in the other channel, or phase cancelling and reducing it, the fact that crosstalk could be at say -40dB (which would be considered very high), that only changes the actual FR itself by a theoretical max of about 0.08dB.
The reason that when looking at headphones the FR is for the most part all you usually need to look at is because they are almost always minimum phase devices, and a completely linear-time-invariant system, so there’s almost never any unpredictable or unusual changes occurring besides what’s described by the magnitude response itself (besides a couple IEMs that have been shown to behave as acoustic expanders for example). But with a DAC there’s a lot more stuff that can be intentionally or unintentionally altered without changing FR itself.
Even from an unintentional standpoint, an audibly high level of jitter for example won’t directly change FR since you’ve just got X amount of jitter added no matter what you’re playing, and so the magnitude of any given sine is still going to be the same.