The issue is specific to certain Haswell-based system configurations.
Haswell introduced new, extremely low-power states called C6 and C7. The processor virtually shuts down in these power states, placing loads as low as 0.05A on the +12V rails. Since it's usually only high-power devices such as the processor and graphics card that draw power from the +12V rail, some low-power desktop builds that rely entirely on integrated graphics pull virtually no power on the +12V rail, while other system components continue to pull significant amounts of power from the +3.3V and +5V rails. This is the cross-loading situation you described in the question.
In group-regulated power supplies, voltage on all rails is regulated based on the total load on each of the rails—the supply compensates for voltage drop on all of the rails as overall load increases (regardless of which rails are under load). Before Haswell, this was never an issue because most older systems placed a nontrival load on all of the major rails. However, in a cross-load situation like the one described above, group regulation can cause the voltage on the +12V rail to be overcompensated to the point where it falls outside of the ±5% voltage tolerance required by the ATX12V standard, exceeding 12.6 volts, while the +5V rail and +3.3V rails may experience excessive voltage drop. The +12V rail may also exhibit excessive noise (ripple) when a group-regulated supply is cross-loaded in this manner.
A properly-designed power supply will detect this overvoltage condition and shut down. However, some very cheap designs may not have this kind of protection and allow the +12V rail to go well out of spec, potentially leading to hardware damage. Even if it didn't go out of spec, a voltage that is consistently way off (not to mention excessive ripple) isn't exactly good for the longevity of the hardware (and remember that office PCs are often idle much of the time, meaning that this cross-loading condition can persist for extended periods of time).
Most modern power supplies use different approaches of generating the +3.3V and +5V rails that eliminate this issue, such as by generating only a +12V rail on the "secondary side" (transformer output) and deriving the +3.3V and +5V rails from the +12V rail through DC-DC conversion, or through independent regulation of each rail. A workaround for this issue on group-regulated supplies is to disable the C6/C7 power states in the system firmware (BIOS or UEFI), but you'll lose the power consumption benefit of these states.
HEXUS has an example where an older group-regulated supply, the be quiet! Pure Power L8 500W, performs poorly under a cross-load test intended to simulate Haswell C6/C7 operation. Notice that the +5V rail nearly falls out of spec at -4.8% while the +12V rail rises to +3.3%:
[...] setting the 12V to practically nothing, imitating a C6/C7 state for a Haswell CPU, forces the 5V line to nosedive by just under five per cent, thus getting very close to the minimum limit mandated by the ATX specification.
More information about the Haswell cross-loading issue can be found in this Corsair article. The issue was first reported by VR-Zone.