Nothing in the Bible says that everything true has a corresponding Bible verse that proves it. However, consider: God gives grace, grace can prevent sin as well as cleanse from it, grace can sometimes be irresistable (some *Protestants* say it always is), Jesus Christ is God, Jesus perfectly obeyed the law, including the commandment "Honor thy father and thy mother."
So, in short: God could have preserved Mary from sin, and we know that He honored her perfectly. In what way would He have "honored" Mary by letting her sink into sin when He could prevent it?
That's the best 50 words of less explanation for Mary's sinlessness I have ever read!