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Based upon the fact you have stated your employer would not be obligated to pay the credit card. However, I am concerned that the facts are accurate. If the credit card is issued under your name and under your credit it is not a corporate card by definition.
Just because the card has your name on it does it mean you are the only obligor. Generally with corporate cards the credit is issued under the corporation's credit history and the employee is identified as an authorized user. This actually means that the company is liable for the debt as the card was issued to the company and the employee is only the authorized user. One easy way to tell is if you get a monthly statement with your name on it you are generally the owner of the card and the signer on the account, not an authorized user.
If however you are right on the fax and this is a credit card issued under your name based upon your credit history billed to you and has nothing to do with your company and your company has no obligation for the same.
Based upon your updated information I did not see how your company is liable for the debt issued to you under your credit. I would suggest contacting the card and asking them for the basis as to why they are seeking to collect from your company. Whatever basis to identify ask them to produce a copy the documents supporting that basis. I would further advise credit card that no payment will be issued absent this information being provided and reviewed.
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