once i called in for a male client, and i was asked for my birthday. i know it is on the PDF my client gave me, but i could not find it, so i said "well, could you wait a second? i will be right back." from that on, i only communicate with broker via email.
You're trading someone else's account without authorization being filed with the broker? That's pretty dangerous. If, OTOH, you have correctly filed a trading authorization, there should be no issue. It's not just the gender of the caller that has to be verified, after all.
I had an experience like this once, with a liquid stock, placed about 40k didn't go thru, phoned the broker asking wtf and was told the trade disappeared into the ether. Actually ended up being got filled at a better price, broker said it can happen but is very rare. Something to do with the routing of the order.