Patio misunderstood your post. You certainly recommend testing it under load; Patio must have believed you meant to have this test performed when the PSU is unconnected from the PC load.
I thought he might have been making that mistake. No load testing is also why power supply testers are so close to useless. It can report a defective supply. But it cannot report a supply as good. A power supply tester can easily report a defective supply as good because the test is conducted without load.
How does the meter verify all components of a power supply 'system'? Nothing is moved, disconnected, or modified. Best test is a system accessing every peripheral simultaneously (multitasking). Then any defect in that system is made obvious by multimeter numbers.
A defective power supply can even boot a computer. Only way to find that defect before it causes problems tomorrow or next year - mulitmeter numbers when supply is fully loaded.