1-If we want to understand the true meaning of that sentence we will have to take 'John' to mean 'John the Baptist'. In an article in ABC magazine, Professor Harrison has suggested that.
Could 'Professor Harrison has suggested that' mean: Professor Harrison has suggested that 'John' means 'John the Baptist'?
I think 'that' could also refer to the first sentence as a whole: Professor Harrison has suggested that if we want to understand... we will have to ....
I am not a teacher.
It is not clear. A plain reading makes "that" mean the sentence as a whole, but the reader gets the feeling that that's not what is meant. Doubt remains.