No, they don't fill themselves. This is why you need to give them a few days heads up if you want Nitrox.
I swear everyone, if you saw this lady cracking all these valves and moving tanks all around every morning you would also say WTF? Reminds me of that animated movie of that squirrel looking for a acorn then trying to find some place to stash it (lol)
It does sound like she is going a little over the top however the way BA just sits dozens of tanks on a mat on the sidewalk, none of them with caps, with no indication of which are full or empty, does not inspire confidence. When I return tanks from a shore dive the guy just says to leave them at the back but maybe the guy is not there when a diver returns and leaves it in the front? They could at least have a different color mat with a sign 'Leave empty tanks on orange mat'
Anyway, it still sounds like her best solution would be to tip the BA guy to find her a well-filled tank and label it for her.