If their suit is still pending and scheduled for trial, then yes, they can include as part of the asserted debt any interest, collection fees, and/or attorney/court costs. It will then be up to the judge to make that determination if the court finds for the plaintiff and awards a judgment.
Sending them an amount that you consider the full principal debt is not a binding contract that mandates dismissal of the civil action unless it is clear that both parties have agreed that the amount discharges the entire obligation.
They have apparently stated that they do not, and thus it is not a binding contract that mandates discharge of the debt and dismissal of the legal action.
Do you have representation of an attorney, or are you handling the civil suit yourself?
" I requested the debt be validated, along with the amount to be paid. I paid the amount via cashier check through certified mail."
Got this in writing from them? If so, and you paid this amount, the judge will rulke in your favor. They are up-charging you after the fact.