Your DAC will display the sample rate as set in Audio MIDI Setup unless your Player software automatically sets the correct sample rate for each file as it is played. [iTunes will not do this but there are add-ons that will, along with other music players].
The Audio MIDI Setup example below is from my office Mac so you won't see a DAC listed. On your Mac, click on the DAC in the left column. Whatever the sample rate is set to in Audio MIDI Setup is what will be sent to your DAC regardless of the file sample rate. Try it. Now change the sample rate in Audio MIDI Setup. View your DAC and note the sample rate it shows. It should match what you chose in Audio MIDI Setup.
You need Player software that will automatically and correctly set the sample rate for each file you play.