I do not blame you for being skeptical. I would be too regarding the authenticity of your sources.
Personally, I believe it because my teacher, the late Great Master Xuan Hua said so. He would not lie to me nor has he ever lied to anyone about Buddhism.
Furthermore, I consult the original Buddhist Scriptures known as the Great Treasury Scriptures 大藏經. They are recognized by all Buddhist experts as the indisputable teachings of the Buddha.
After you have planted more blessings with Mahayana, you too will believe.