The waitress's own accounting of the incident is exceptionally self serving and false. The signature as originally posted was quite legible. Her original accounting of the incident was completely fabricated because she didn't actually serve the table, though she represented herself as if she did.
For example, the customer's name, Alois, is a man's name, but the customer was actually a female with a male's first name. The waitress asserted that the customer was a man. When she later found out she was wrong she backpeddled and claimed she knew that but that she was protecting the customer's identity. However she publicly posted the customer's name and location, enabling people to track down the customer and begin threatening her.
Another detail she got wrong was claiming the customer left no tip. The customer left the tip as cash on the table, as most people in the US do, and something that most servers prefer, rather than pay it as part of the bill. The restaurant also though double charged the customer for the tip, meaning the customer ended up paying 36% rather than 18% on the bill as tip. Because the waitress had not served the table she assumed that the strike out of the tip line meant the customer left no tip at all.
In short, the waitress violated a customer's privacy, lied about the customer publicly defaming her, publicly ridiculed her religious beliefs, and instigated an internet mob riot against the customer which continues to this day in the form of threats and harassment and has caused the customer severe mental anguish. If I was an attorney in the area I would be preparing a large lawsuit against the restaurant at this time, and I would certainly prevail in court.
Her firing was completely justified and her complaining about being fired in the media and claiming herself as victim when she was the bully is absolutely outrageous.