I've heard before that if a signature card does not specify what the individual's relationship is to the account, then the individual is considered an owner. For example, if a signature card simply said 'John Doe' and not something like 'John Doe, Authorized Signor', then John Doe would be considered an owner.

Is this true for TN law? If so, any reference to where this can be found in the law?

I don't believe it is specifically addressed in TN law. However, we would take the position that the signature card/account agreement "rules." In the absence of the ownership designation, we would treat it as if John Doe is an owner. You may want to read over the account agreement to see if it addresses this particular situation and/or contact legal counsel.