I've read the book, and found it thoroughly convincing. Whether or not you agree with the theory, it is a fascinating read and I highly recommend it.
I will say this - technically this Chinese fleet - at a time when China was the undisputed technological giant of its time - could have made such a voyage.
If no records exist it is because of the massive destruction of records of the world outside of China after the voyage was made.
China invented book burnings centuries before - "cultural revolution" like events are not new to China.
So of all the theories of pre Columbian contacts with America - the Chinese contacts are the most believable.