The factory ECU doesn't run overly rich if you leave the car standard, but if you start to modify the car (exhaust, intake, turbo etc), then the stock ECU will over compensate, and overfuel. For minor mods you can just get an SAFC, which modifies the signals to the stock ECU, and helps control the fueling.
A well tuned aftermarket ECU will provide the right amount of fuel for the mods it has been tuned for, but if you change the mods it will require to be tuned again.
Hope that helps.