What access rights should an employee grant an employer for a work computer?

For instance, let's assume that the business people come to the IT lab late at night for discussions with the CIO and they use my computer for reading email and general web surfing. In a sense, this means that they are taking full or partial responsibility for any security issues that crop up that get traced back to the employee's machine.

Perhaps the proper way to provide a computer to an employee is to give him full and exclusive use of it while employed.

Only supervised access (such as hardware/software maintenance) should be acceptable.