Kevin, your grammatical analysis is faulty itself. A /reed/ reading that would make grammatical sense: "Did you read the book that I (always) read (on Sunday afternoons)?"

Further, one could argue that your "corrected" example is likewise ungrammatical: "Did you read the book I am reading?". Shouldn't that be "Did you read the book that I am reading?" ?

I'm no prescriptivist, but I think that those who are need to tread carefully.