Does a personal guarantee require a signature? The bank says I consented to the guarantee merely by using the corporate credit card.

My single member LLC (dissolved since 2015) opened a corporate credit card with Bank of America in 2013. I opened the account as the sole officer/member of the LLC and used it strictly for business. The account went into default when my business closed, and was charged off in 2014. Recently, the bank performed a setoff against my personal checking account (opened in 2011) as partial payment, claiming that I am a personal guarantor of the LLC's credit card. The only relevant documentation they've produced is a copy of the business "Cardholder Agreement" pamphlet, which is mailed along with the credit card. They claim that I consented to the Cardholder Agreement by using the card, thus, I am subject to its broad, blanket guarantor and 'right of setoff' language. (Can't paste it here for lack of space.) Without a separate signature, would a judge say the guarantee is valid? And if sued, would a judge require them to prove that I otherwise signed/consend to the guarantee?