"I want to make sure the public understands that I fully support my fiancé, Carmelo Anthony, and stand by him through this ordeal," Vazquez, a former MTV veejay, says in a statement to PEOPLE on Tuesday. "I will always have his back and never refused to pick him up from the police station. In fact, they offered to bring him to me."
Anthony was arrested early Monday morning near downtown Denver, hours after leading his Denver Nuggets to victory over the Houston Rockets.
The NBA star reiterated his love for Vazquez in his own statement to PEOPLE: "LaLa continues to be a rock in my life, she's always been there for me through thick and thin."
The couple have a child together, 1-year-old son Kiyan. Vazquez will soon costar in the movie Let the Church Say Amen and will host and executive produce VH1's upcoming reality show The Sixth Man.