Yea, common-mode computer noise are usually wideband (hissy). Tho sometimes you can hear your mouse or HDD through it.
Can anyone tell me how a bad usb connection added hiss along with the normal signal?
First we have to know what the "good" USB connection is supposed to sound like. Because sometimes the "good" connection is the one that is hissy and we resort to cutting ground connections to remove the hiss.
Common-mode noise happens when the ground (or, the "common", or reference) voltage at the source is different from the ground voltage at the load. The signal voltage, without going into details explaining why, can be assumed to be identical on both ends. So if ground voltage is also the same on both ends, then "signal minus ground" at source is the same as "signal minus ground" at the load and everything is happy.
Now, the computer is a very noisy thing, and this can be easily demonstrated by getting two sound cards inside the same computer to measure themselves. Individually they may measure -120dB SNR, but when measuring each other they can drop to -100dB or less, which make them on-par with onboard audio. That's what having lots of ground current flowing in ground planes can do to SNR. Do remember tho, -100dB @ 2V = just 0.2mV, so this is not a concern for electronics operation; audio just happens to be sensitive.
So when it comes to generating the signal for your headphone, what ground do you think it is referencing to? Not a rhetorical question, because I also don't know how exactly the insides of the DAC/amp/preamp is wired. But let's say it is referencing the ground of the original analog signal. But at the same time, your DAC ground (I'm guessing) is also connected to your computer USB. So what ground is your MOTU at since it is being connected to both? Answer is we don't know. Hence the noise.