Yes, heart rate variability could have lots of causes. So do fever, high/low blood pressure, fatigue, coughing, headache... No disease is diagnosed from a single symptom. The symptoms are clues; indications of possible illness. The next step is to find out exactly what that illness may be.
What was learned in this study is that a variety of wrist-worn heart rate monitors (Apple's being only one of several) could detect very small changes in average heart rate (as they are worn constantly, there are weeks, months, or years worth of readings available for comparison). Those variations correlated well to COVID-19 infections among the study group (healthcare workers). It does not state that this is a way to diagnose COVID, but rather, it's a way to detect several days sooner than other methods, the possibility of a COVID infection. It's a reason to take that swab test, it's not a substitute for it.
You could as easily say that fever can have lots of causes, so therefore measuring body temperatures is a bogus test for (name your illness here). Yet in today's environment, scanning with an infrared fever thermometer is part of routine screening for possible COVID-19. Temperature-taking alone cannot diagnose the disease, but at this particular point in time, due to the current rate of COVID infection in the population, what it does to those who catch it, what it costs to treat those with serious cases, the number of people who may become infected by a yet-untreated carrier... an elevated temperature is a good enough reason to take a COVID test and obtain a proper diagnosis. So, why not an elevated average heart rate? That's one of the core benefits of wearable biomedical monitors.