So you arguing:
1) there is no such thing as a verbal contract?
2) that no company ever makes an offer contingent on screening?

Yes I am taking the story at face value, mostly on the merit of the fact that the EEOC accepted the charge, you are aware that they don't file complaint for every applicant filing a charge, but those that they see are covered by there jurisdiction, including:
"If you believe you have been discriminated against by an employer, labor union or employment agency when applying for a job or while on the job because of your...sex (including pregnancy, gender identity, and sexual orientation)"
https://www.eeoc.gov/field/denver/charge.cfm

And while my assessment is admittedly based on one side of the story, yours is pure speculation based on no statements whatsoever.