Considering how inaccurate some of Fitbit's measurements are( resting heart rate, for example ), I would sue my insurer if I found out they were using that data. My doctor shouldn't be using it either.
RHR is normally measured within the first 30 minutes of waking while lying in bed, which is something Fitbit can determine. What I've noticed is that on days when my RHR that I've measured using their monitor after waking is 54 BPM, they report up to 61 BPM. There's a very long chain on their forum about how inaccurate the measurement is.
Also, one of the critics in the chain thinks Fitbit must be inaccurate after his RHR rose from 68 to 71 after "hiking at altitudes up to 14,200 feet" then fell back to 68. I think this criticism stems from a misunderstanding about how altitude affects oxygen levels and how oxygen levels affect heart rate.
All that being said, even if the devices are generally accurate, there are defects and they aren't designed as medical devices. To the extent you voluntarily share your data with a doctor or insurer (which is the only way they'd get your data), your doctor or insurer should treat it the same way they treat other useful but potentially inaccurate information.
RHR is normally measured within the first 30 minutes of waking while lying in bed, which is something Fitbit can determine. What I've noticed is that on days when my RHR that I've measured using their monitor after waking is 54 BPM, they report up to 61 BPM. There's a very long chain on their forum about how inaccurate the measurement is.