So I think it IS possible for a customer to know that s/he needs a supervisor.
From my call centre experience I'd certainly agree that this is possible. In some cases I'd be hinting as subtly as I can for the customer to ask for a supervisor because they had to access to do things I couldn't. However 9 times out of 10 this is not the case.
When asked why they wished to speak to a supervisor, even the people who needed to talk to a supervisor would then scream down the phone that they didn't want to talk to you, they were only going to discuss this with a supervisor. In my head I'd be thinking "Well Mr/s Customers, frankly I don't want to talk to you either, not talking to you and transferring you quickly will bring up my stats and put me in the running for some nice bonuses." But it was a fireable offence to transfer a blind call.
And the cherry on the cake for these cases was due to high turnover in call centres, I was more experienced than most of my supervisors (who were supervisors as they were full timers) and tended to have the error fixed before you were even transferred.