Update: My mother refused to sign the agreement and stood her ground, stating that she would go to trial if need be, as she falsified nothing.
She had no money for a lawyer, but refused to admit to something she didn't do.
She was offered a new agreement days before the hearing that omitted the inaccurate recording, falsifying bit.
She gladly signed it and has to take a couple of courses next year as penance.
Everything worked out in the end, but apparently they wanted her to buckle under the pressure and sign something that would've been worse for her rather than simply admitting that they had nothing to suggest she inaccurately recorded or falsified from the start. I have no clue why they wanted to punish her so badly, but end the end, holding out and seeing it through proved the right thing to do.
Thank you for all the advice you gave, it was quite valuable to us in this matter.