With all security, there is always a weak point. As ever, the onus would be on you to make sure that you were relatively secure whilst using live chat or phone. Not having a go at you but the trend amongst alll providers of services are writing into their t&c's. Just this morning, the amended t&c's of my bank mentioned that I basically need to memorise the pin numbers and I'm not allowed to use any form of electronic method of storing the pin.
But there are a number of things they ask for to confirm your account like phone number, date of birth etc before getting to the secret question. You could always change the question immediately afterwards if you feel its been compromised.
