Here's an example of "parasympathetic saturation", highlighting an important limitation of supine (or sleeping) HRV.
When HR is <55 bpm, HRV often decreases, despite high parasympathetic activity. Thus, HRV becomes an invalid marker of parasympathetic control.
In the example below, RMSSD is 25 ms higher in the standing position despite a higher HR and the well-established vagal withdrawal induced by orthostatic stress.
This explains many (not all) cases of low HR with low HRV among fit individuals.
To overcome this issue, and due to its superior sensitivity to stress/fatigue, HRV is best measured after waking in the standing position, IMO.