Despite protests to the book on Carly Simon’s website, “More Room in a Broken Heart’’ appears largely rendered out of love and respect for Simon and her legacy. Davis first encountered Simon on television in 1964 when she and her sister Lucy performed as the Simon Sisters. He was later astonished to realize his Boston University classmate Peter Simon was their brother. Thus began a decades-long association with the Simon family that infuses Davis’s accounts with a cozy intimacy.