I had a similar experience, actually, and it boils down to the fact that the HemoCue is not FDA authorized for home use -- it is meant for doctors, blood banks and emergency rooms -- so it doesn't have a proper identification number, and that all means that reimbursements are up to the insurance company's sole discretion.
Now, to my knowledge I was THE first SCLS patient to use a HemoCue device for self-monitoring purposes, so I expected problems. To begin with, in those days (2009) it wasn't sold on the Internet, and it had to be ordered by one of my compassionate doctors, so he bought it and then I reimbursed him. But I had hoped that times would have changed since then, just as they have in terms of obtaining approval for a course of (expensive) IVIG therapy.
The good thing is that now it IS more available, and the price has come down by almost half from the nearly $1,000 they charged backed then. This is largely because by now another company has invented a non-invasive device that allows blood banks and emergency rooms to read your Hgb count (and other things) just by touching one of your fingers. (Sorry, that one is really expensive and is hooked up to special monitors.)
So it boils down to this: Do you want the peace of mind and convenience that comes from being able to test yourself at any time of the day or night, weekdays or holidays, at home or work or while traveling, to see if you are or are not having an episode? If the answer is Yes, then you may want to go ahead and just buy it with your own money. (They sell them on Amazon for $400!). Once you've paid for it, the supplies are a few hundred dollars per year on top of that.
In my case, I could afford it but I would have bought it even if it meant not going out to fancy restaurants for a while, and it proved to be a life- and limb-saver -- until IVIG came along, that is.