The reason S.N. Roy is attributed as the author of "The Story of Indian Archaeology" is based on historical records and bibliographic information. S.N. Roy was a known archaeologist who contributed to the study of Indian archaeology, and he is the recognized author of this particular book. This attribution is established through the publication's title page, the author's preface or introduction, library catalog information, and references in academic and historical literature. It's essential to verify such information through reliable sources and bibliographic records when determining the authorship of a particular book.

So, the correct option is [3].