It's not bit perfect if the volume adjustment is being done in software, but is if the volume adjust is done in hardware.
Now it's my turn to be unsure - but I think you've got it now but maybe not for the right reasons.
1) If you change the volume in the digital domain (software) then it is no longer bit perfect.
2) If you change the volume in the analogue domain (a hardware amplifier) then it is in a way bit perfect - provided point 1 above has been met.
The real point I am trying to make is that you really shouldn't worry about 'bit perfect' at all.
Please let me try and explain. You can help me by telling me whether I have succeeded.
Your ears are designed to detect small changes in air pressure over time. Your brain translates this information into sound.
Now cast your mind back to high school physics class........
If you move a magnet in a coil of wire this generates a current - change of voltage over time - This is a microphone.
If you pass a current - changing voltage over time - through a coil this will cause a magnet to move. This is a loudspeaker.
So you can now envisage analogue audio not as changes of pressure in the air over time but as changes of a voltage over time in a conductor (wire).
A perfect analogue amplifier increases those voltages evenly. The sound doesn't really change. It just gets louder.
There is no such thing as a perfect analogue amplifier. They all add some distortion. We will not cover why now as it's not relevant to the current discussion.
An attenuator does the same in reverse. Reduces all the voltages evenly over time. This can be done without adding distortion.
Now we get to digital audio. What an analogue to digital (ADC) converter does in effect is measure the voltage in a wire at very precise and very small time intervals.
44.1 thousand times a second in the case of red book standard CD. The accuracy is determined by the bit depth. Again for CD this is 16 bits.
So the voltage at any one instant becomes a number. In fact it's a pure number - a ratio.
So what was originally a measure of air pressure at one instant in time and then became a voltage in a wire can now be envisaged for the purposes of our explanation as a number between 1111111111111111 & 0000000000000000. You will need to do some further research of your own to fully grasp the details but for now that will do.
So a what a digital amplifier does is increase all the numbers by a set amount and a digital attenuator decreases the numbers by a set amount.
An digital to analogue converter (DAC) does the whole process in reverse. Translates the numbers back into a voltage. The analogue amplifier increases the voltages to your desired listening level. The loudspeaker translates the changing voltages back into changes in air pressure. Your ears measures that and your brain interprets the result as sound.
The real miracle in all this is not the technology - it's your brain. As we can now see if I've succeeded with my explanation is that sound is in effect one dimensional. Almost a series of loudnesses. Frequencies - notes, harmonies, words are not as such recorded. It's your brain that creates them. Pretty cool eh? Well done evolution.
So the upshot is - don't worry to much about about bit perfect digital audio. Set your media player volume control to about -3dB (about 95% of maximum) and all will be well. All that is happening is that all those huge numbers in the samples are being reduced by a small set amount and it's being done to an accuracy of less than 1 part in 2 raised to the power of 16. That is well beyond your ability to detect - your brain is clever - but not that clever.