Many thanks to everyone for your help.
In fact, I have a Dell Studio XPS 8100 desktop. This computer probably has a power factor correcting (PFC) power supply. I say 'probably' because no one I have corresponded with at Dell seems to know; however, the Studio XPS 9000 does have a PFC power supply.
My computer's power supply is rated at 350 watts, which is certainly far less than its maximum capacity, since 115V times 8A is 920 VA. As many of you have observed, it doesn't seem correct that the maximum current is as high as 920 watts...that's with a power factor of unity. Even with 80% efficiency...736 watts?
Of course, the PSU delivers far less during typical service. But a PFC PSU can draw its full capacity when first started. At least, that's what I understand.
How this relates to a UPS: If the transfer time (to battery power) is long enough - as little as 8 ms, according to what I've read - a PFC power supply will draw its full inrush current from the UPS, or attempt to. This can cause the UPS to drop its load (to say nothing of the computer user.)