Veterans E-Health & Telemedicine Support Act of 2013 or VETS Act of 2013 - Allows a health care professional who is authorized to provide health care through the Department of Veterans Affairs (VA) and who is a licensed professional to practice at any location in any state, the District of Columbia, or a U.S. commonwealth, territory, or possession, regardless of where the professional or patient is located, if the professional is using telemedicine to provide treatment. Allows such treatment regardless of whether such professional or patient is located in a facility owned by the federal government.