How have they decided the periphery is always about safety hazards?
I wondered this. I am as likely to be looking for cats (though by the town centre, more likely to see rats,) or currently under street lights, see if the crocuses are out yet to come and see them in daylight. And sometimes there's new graffiti, much of which is dull, but there's occasionally something which makes me smile.
I look round more in daylight, too - I look at wildflowers and birds and things - I just spot a lot more than male colleagues I've walked with at lunchtime do, because I was brought up to look for signs of wildlife and plants and so on, and they're there even in an urban environment. I am most likely to be the one saying, "look at that!" (And they'll respond, "how do you know what that is, what's interesting about it?") Some men do do it more - a professional ornithologist I knew often spotted more birds than I did - because he was looking for, and recognised more signs of them than I did.
But also, don't women have better peripheral vision than men on average? So we're more likely to notice movement and will turn to look at it - partly as an instinct to check it's not a threat but just a leaf moving in the breeze, but also we fo just see more peripherally.
I have not read the report, so they will cover this, and I am not saying women don't pay more attention when they walk home - we all know we do. It might not be the only reason - it isn't for me. I take note of the environment I'm passing through for interest as well as safety.