Update:
On maybe the fifth try, it worked. But now it's requiring my contact list to proceed. The app itself on the home screen is just called "rn-fetch-blob" (i.e. a default react native project). I'm not going to give contact list access to an app that didn't even bother to give itself a non-default name/icon on the home screen. I think the app needs a little more time in the oven before you have other people try it out.