This isn't to say that all people are completely trustworthy, but sysadmins have by necessity nearly unlimited amount of access so they can do their jobs. If you're worried about security (which you shouldn't be faulted for, seriously...most don't pay attention to it) you may want to work with your sysadmin to install safeguards for auditing.
Have all procedures documented, as should be part of his job. If he were hit by a disgruntled user's car tomorrow you should be able to have a new sysadmin get up to speed fairly quickly with the policy and procedure guides.
Also, your sysadmin shouldn't mind having safeguards in place for protecting his or her actions from fudgey fingers. Sudo logs things. System passwords should be kept safe and accessible if needed, but only to people who actually need it (and it should be known if someone wants to get access to them.)
The sysadmin needs enough freedom to do his job and feel like he or she isn't being second guessed all the time or mistrusted (or why would you have hired him?) Let the sysadmin do the work, but know that he or she can be audited if need be.
It's a red flag if they're too secretive. But it's a problem if management won't let go of the reigns too. And it's worse when people in management keep sticking their fingers into IT if they're not IT people (not saying you're not, since I don't know what you do...but it can be a problem when engineers and/or programmers, who think they know what it's like to do sysadmin tasks, really kinda don't, and insist on doing things their way...)