I think everyone is aware that you may not know the system as well. They also probably know the coverage that their application is given and know deeply themselves that it is not well formulated and documented. They may just be using you to get the QA 'formalities' out of the way.
Obviously this isn't the way to go. For your career and integrity as a QA.
So what I would do is first is pound them with questions so you can understand the system. Be straightforward. For example "I'm flying blind testing this new feature. When you have a sec can you please walk me through ___"
Second, *everyone* knows a new resource is an initial time investment. Kindly remind them if they want to pretend otherwise. Be straightforward. "I want to contribute some value to testing this application but I'd need some time learning the application." Just be upfront and state the truth - which is you can better contribute if you know more so they need to suck it up and teach you everything first. Just don't say anything cheesy like 'help me help you' or anything not really sincere haha...
Third, addressing the elephant in the room is a QA pre-req. So not having the comfort to do the above is a negative for a QA. Being comfortable with what you don't know makes a great QA. Being pigeon-holed and silo'd in any 'fear' of any form of bureaucracy is not an env a QA can thrive in. In reality if that is the culture of the company - then they are not ready for a real QA resource :P