In Chapter 19, a song says, 'I do not believe in anything without Rama.' Does this imply that Sai Baba's path rejects devotion to any other deity or form of God?

This is a misunderstanding of the text's context. The line 'I do not believe in anything without Rama' is from a song that the author heard a man named Aurangabadkar singing. As recounted in Chapter 19, this was not a declaration by Sai Baba himself, but a song that coincidentally mirrored the author's own private resolve to chant Rama's name. In fact, the same chapter highlights Sai Baba's inclusive and non-sectarian nature, quoting him as saying, 'Allah-Malik, Allah-Malik' (God is the Master). The event is presented as an example of how Sai Baba encourages a devotee's specific good thoughts and confirms their resolve, rather than a mandate that all devotees must exclusively worship Rama. The true teaching is about the power of undivided devotion, whatever its focus.