Dear Cynthia,
The rules about articulation placement are solidly established and differ depending on whether a staff has a single voice or two. The extract you quoted from Read is the rule as it applies to a single voice. When two voices share a staff the articulation placement is reversed (think about what would happen when both voices have articulations - they would all end up in the middle of the staff if placed on the notehead side, which would be very difficult to read). I would be very surprised if Read neglected to mention this exception to the rule, so maybe it's worth rereading to double check. My library has this book in storage, so it will be a number of days before I can check myself.
Kevin