Answer:
"Business account" leaves out too much information. Is it a corporation, partnership, LLC, sole proprietorship? Relying on TIN's is unwise. Some of the bankers who get them don't know what they are doing.
If it was a sole proprietorship, the answer would have been: "Maybe." It would depend on the law of your state and the verbiage in your contract.
If the business was an actual legal entity, the answer would have been a flat "No."