The point is not whether enough identifying information could be obtained this time, but rather the fact that she (arguably) did not really consider that when posting the image, and that she could do it again (and this time reveal enough identifying information). Had she tilted the camera a bit further down the whole signature would've been visible.
Imagine an employee in a company accidentally leaks some user data, which does not really contain personally identifying information. I don't think it's completely unjustifiable to fire this person even though no damage was done.
Of course the owners of the restaurant could've dealt with the situation a lot nicer (warning her about the potential danger instead of firing her). But I don't blame them for taking the more drastic measure that they did (not saying that I would've done the same).
Imagine an employee in a company accidentally leaks some user data, which does not really contain personally identifying information. I don't think it's completely unjustifiable to fire this person even though no damage was done.
Of course the owners of the restaurant could've dealt with the situation a lot nicer (warning her about the potential danger instead of firing her). But I don't blame them for taking the more drastic measure that they did (not saying that I would've done the same).