I'm a retail store manger and I don't buy that story.
We get people coming to us all the time complaining about what an employ did or didn't do, most of them looking for a discount and 99% of the time its all bullshit. If I fired someone just because a customer complained about them, I'd be running the store by myself.
Hell, I probably wouldn't fire an employ for dropping the fbomb if it was in general conversation unless it was direct at a customer UNLESS I was already LOOKING for a reason to fire someone.
If thats what they fired you for, they were already looking for a reason or someone didn't like you.