Not sure where you read it. But Background check and eligibility are two different things. Your admissibility under IRPA gets assessed with background check. However, your entire application is subjected to a reassessment if the final approving officer feels otherwise - this is uncommon though.
If they cleared your eligibility the case processing officer feels convinced about your work exp, education, etc. For most people, unless they actually misrepresented, there's no reason to worry about eligibility. It is very very hard for IRCC to reject applications who were truthful in their application. It should help you put a perspective on how helpful the system is for genuine applicants.