My company started hiring office assistants a couple years ago. The rationale is pretty straightforward: since good engineers are hard to find, free our engineers of non-engineering tasks so they can spend more time on engineering.
Most of the part-time office assistants do customer support or sales processing, but one of the office assistant positions is special: the person hired for that position does most of the purchasing and many other miscellaneous tasks that several of the full-time employees (including myself) used to do. The person in this position has everyone's corporate credit cards (which I suspect is a violation of the credit card terms, but I'd have to check on that) and various online accounts (again, possible violations of the TOS, especially for purchasing- or banking-related sites). Now I'm being asked to transfer administrative access to that person for other accounts. So far, I haven't explicitly been asked to transfer management of the employee benefits to the assistant, but I suspect I may be asked to do so at the next renewal.
The concern I have is that someone with administrative access could remove everyone else's administrative access, change the contact information, and lock us out of our accounts. If the person also eventually manages the employee benefits, they could cancel employees' benefits. I trust the current office assistant not to do any of this, but I'm concerned that a future person hired for this position might do so, especially if we continue to grow. (What if a con artist passes our interview process?)
How much power do you give your part-time employees over the administration of your company? Are my concerns reasonable, or am I just being paranoid?
Never have a single person with administrative privileges on your accounts. Always have at least two (for example, the person actually doing the work, and the controller or the CFO).
Also, make sure all the accounts are in the name of the business entity. The person with the administrative access is a mere representative, if the assistant abuses the power you can fire that person and reinstate all the access privileges. Since the account belongs to the entity, some matters will require an entity decision (for example - board meeting resolution, change in the LLC operating agreement, etc). Banks require proofs of such changes before doing anything (for example, changing account ownership).
If you can set the accounts so that certain operations require more than one signature - do that. That would limit a possibility of embezzlement or fraud.
These are checks and balances that should be implemented in your company. Public companies must have certain checks and balances, but private companies are not required by law. Still, you can chose to implement some that would not make your life too complicated, yet will make you more secure. You can ask your accountant for more specifics. Many accounting firms provide advisory services to help with exactly these issues.
You're not being paranoid. You're asking the questions you should be asking.