Q: How can you say that the heart is on the right when
anatomists find it on the left?
M: It is not denied that the physical organ is on the left, but the Heart of which I speak is on the right. It is my experience.

No authority is required.

But still, you can find confirmation in the Sita Upanishad, where there is a mantra that says so.

The whole cosmos is contained in one pinhole in the Heart. A tiny hole in the heart remains always closed and is opened by vichara. The result is 'I-I' consciousness, the same as samadhi.

Conscious Immortality, 166

At the time of retraction, for the sake of rest, when She rests on the right side of the Lord’s chest, in the shape of Srivatsa, She is the power of Yoga.

- Sita Upanishad, v 35

Srivatsa means "beloved of Sri", the goddess Lakshmi. It is a mark on the chest of Vishnu where his consort Sri Lakshmi, or Sita, resides. It is said that the tenth avatar of Vishnu, Kalki, will bear the Shrivatsa mark on his chest.