That's unrelated. This difference is the inter-aural or inter-channel difference and 16/44.1k can capture that to much greater precision than microseconds.

Some math [1]

44.1k file containing pulses with sub-sample delays [2]

Something similar, but square wave, and nicely showing that timing precision actually depends on bit-depth and not the sampling rate [3]

Some practical experiments with capturing the playback of such files and verifying that the delay is preserved: pulse [4] and square [5]

[1] https://troll-audio.com/articles/time-resolution-of-digital-...

[2] https://www.audiosciencereview.com/forum/index.php?threads/t...

[3] https://audiophilestyle.com/forums/topic/58511-time-resoluti...

[4] https://www.head-fi.org/threads/can-you-hear-upscaling.97295...

[5] https://www.head-fi.org/threads/can-you-hear-upscaling.97295...