The only motives that influence all human actions arise from self-interest.
Conclusion
Self-interest is the chief (#1) influence on human action.
Evidence
The only motives that influence all human actions arise from self-interest.
Evaluation
Both the premise and the conclusion are about "self-interest" and "human action" and "influence", so we should subtract the commonality and focus on the variation.
If X is the only thing that's part of every action, does that mean that it's the #1 influence on action?
Does "most omnipresent = #1 influence"?
Maybe. But maybe love is a motive that influences only 98% of human actions, but when it's present, it has a stronger influence than self-interest.
Goal
Point out the language shift from "most omnipresent" to "most influential" or raise the possibility of a counterexample such as love, which may not influence 100% of human actions but still might end up being the #1 influence on human action.