As for the test she flunked ... Richardson says she recently found out her biological mother died, and she used marijuana as a way to cope with the stress and pressure.
For what it's worth, use of recreational pot is legal in Oregon -- where the trials were run.
USATF released a statement on the decision Tuesday afternoon ... saying it's "incredibly sympathetic" towards Richardson's situation ... but it would be "detrimental to the integrity" of the organization to bend the rules a week before the Games.
"All USATF athletes are equally aware of and must adhere to the current anti-doping code, and our credibility as the National Governing Body would be lost if rules were only enforced under certain circumstances," the statement read.
USATF praised Richardson for owning up to her actions and agrees that the World Anti-Doping Agency's guidelines need a makeover ... but until then, athletes gotta play by the rules.