The claim is directionally supported: a major review of the literature says public trust in elections reflects whether election processes meet democratic standards, and it identifies electoral-management performance, integrity, and election experiences as important drivers of trust. Experimental studies also find that trust rises when voters are informed about election protections and that delays, misinformation, or attacks on election administration can reduce trust. But the evidence also shows trust depends on other factors too — especially partisan cues, winner/loser status, and broader political context — so "everyone following the rules" is an important contributor rather than a fully determining or exclusive cause. Sources: "Global Crisis of Trust in Elections" (Public Opinion Quarterly) (academic.oup.com); "Restoring Trust in US Elections through Effective Election Administrator Messaging" (Public Opinion Quarterly) (academic.oup.com); "Voters distrust delayed election results, but a prebunking message inoculates against distrust" (PNAS Nexus) (doi.org); "Can Public Information Campaigns Restore Trust in American Elections Across Polarized State and Party Lines?" (SAGE / Journal article) (journals.sagepub.com)