The airline may deny boarding without fine if "there are reasonable grounds to deny [...] boarding" so I would focus on the grounds for denial.

At boarding, you were informed that something was wrong with your credit card and so you were denied boarding because it was too late to fix this problem. I would focus on the reason for waiting until boarding started before the airline informed you of the credit card problem. Why couldn't they inform you of the problem already when you checked in by asking you to go to a check-in counter? If the payment problem didn't occur until after you checked in, why didn't the airline try to call you to sort out the problem? I do not think that they have reasonable grounds to deny boarding unless they make reasonable effort to inform you about the problem until it is too late to fix the problem, unless the problem didn't become known until it was already too late. Most payment problems ought to be known already when you book your ticket.