Only then will a womans fertile woman actually play a role so close to cessation of bleeding

Correction: ...will a womans fertile WINDOW...

actually, no every body is the same in terms of the workings of the follicular and luteal phases- as well as conception and implantation timeline.  The follicular phase can be influenced by outside factors (stress, illness, medications, etc) that can lead to a delayed ovulation or even annovulation (no ovulation).  The luteal phase is the constant part of the reproductive cycle (12-15 days depending on the individual cycle but most often 14 days) and if it is less than 10 days the woman is considered to have a luteal phase defect and is treated accordingly. 

 If someone is truly on their period then their lining is being shed- giving a possible embryo nothing to implant to- which is how the "Plan B" or "the morning after pill" operates: by forcing the lining to shed.