[always_good]

>requires the attacker to know you do this

Nah, "well, it kinda looks like random characters" is information a support rep will give you.

Welcome to social engineering and info escalation.

[ubernostrum]

If the support rep is just giving away enough info to figure this out, there is nothing you can do to protect yourself against the company's policies.

[always_good]

Yes, which is why social engineering is going to get a whole lot worse before it gets better.