I actually have "your fertility signals" by Merryl Winstien sitting right next to me at the moment.
The reason it's not considered "safe" is that the blood can hide fertile mucus, so it can be hard to tell whether or not you're fertile.
This book says that on the last day of your period, when it can be considered "spotting", if you are otherwise dry, you can consider yourself infertile.
Saying you can get pregnant any time is ridiculous. You can get pregnant if you have sex during the few days before ovulation, while fertile mucus is present to protect the sperm until you ovulate until 4 days or so after you've ovulated, at which point your body temp. will spike.
The trouble isn't that you can get pregnant "anytime",it's that these days many womans cycles are super wonky due to all the stress, and crazy hormones in our food, and artificial lighting while we sleep.