The words mean that the person said something (an opinion or belief), but did not say it often.  So, that person was not believed (or taken seriously).

[我偶爾聽他那麼說，可是我不認為他是來真的。]

句中 on occasion 做副詞用，意思和 sometimes, but not often 相同。當某個人態度認真，所言不虛的時候，我們可以說：He was serious.