You cannot think of a compromise as being a simple state of either your compromised or your not. There are different levels of compromise and and different levels of protection to either limit the compromise or alert you to when you have been compromised. While we appear to be seeing an increase in active, targetted 'cybercrime' type compromises, it is important to note that many, some might even suggest a majority, of data compromises have occurred through accident and misconfiguration rather than deliberate 'hacking'. While still limited, the fact your password is hashed provides some protection when that sys admin accidentally changes the permissions on a key file and someone is able to download a copy of the sites password database.
Your point regarding system administrators is valid. This is where reputation becomes very important. If you use an email provider you don't know and have no confidence in, who has no real reputation, then you should be either very concerned or just accept that there is a high chance that a sys admin is reading your email. The point is that in life, we often have to trust people we don't really know that well. We do this all the time. Last time you were at a restaurant, did you trust the waiter with your credit card? How much trust do you place in the receptionist at your medical clinic?
Often we will guage this based on reputation and cost. We know that good security comes at a cost. Unfortunately, what a lot of people fail to recognize is that 'cheap' or budget service providers must cut costs somewhere and all too often, that somewhere is security.
Bottom line is that on most systems, at some level, there will be someone who has complete access to all your information and they don't need your password (there are some situations where this is not strictly true, but they are in the minority, so lets just assume this is not the case). The question then becomes one of whether you trust this service provider with your private data. Are you paying enough to expect a confidential service? Does the provider have a sufficient investment in reputation that they will take sufficient measures to ensure your data is sufficiently protected i.e. adequate vetting of staff, good audit trails and sufficient auditing of processes to ensure business processes are adequate and are followed etc.