Understanding how it takes almost 2 weeks of hormonal buildup and biofeedback to cause ovulation and then the post ovulation until your next period is anywhere from 12-17 days for most women, its just not something that occurs from being around other people. It takes hormones to change these cycles.
I am not sure how this is possible since our periods do not come psychologically. When you think of how periods work, we don't send out a vibe that tells someone elses ovaries to sync up with our own. Or else infertility would be contagious, or anovulation would be contagious that is.
More than anything i think if you use any other possible physical thing that would come at frequent intervals you are likely to "overlap" someone elses event given some time on a calendar. For example, if you had a sinus infection every four weeks (approx.) and so did several other people in your household or friends... you are likely to be battling a sinus infection sometimes at the same time. It's just math probability.
Given all the periods one has in their lifetime and how many menstruating women there are in the world, its not all that unusual to think of 2 random women you know having a period at the same time.