Final answer:
True, crossing-over requires precise alignment of homologous chromosomes during prophase I for the exchange of DNA between nonsister chromatids.
Step-by-step explanation:
The statement is true: for crossing-over to occur, homologous chromosomes must align precisely early in prophase I so that nonsister chromatids can exchange corresponding segments of DNA. During prophase I, a tight pairing known as synapsis takes place, and this precise alignment is critical for the synaptonemal complex to facilitate the exchange of chromosomal segments, a process referred to as crossing over. This unique combination of genetic material contributes to the genetic diversity found within offspring.