Not accurate.
Until the early 90s and the rise of Hamas the most active Palestinian militant groups were secular, some were even Marxist/Leninist (as in, officially areligious).
Fatah, in control of the PLO, has always been secular and the second most active Palestinian militant group during the 1970s was the Popular Front for the Liberation of Palestine, a Marxist organisation led by a Palestinian Christian.
Political Islam as a force in Palestinian politics started in the 90s and only really became a big thing during the second intifada in the early 2000s.
The Wikipedia page [1] makes for an interesting read if you want to understand more about the Lebanese Civil War and the many groups and foreign interests involved in this tragic conflict. As for the Palestinians, they had a large refugee population established in Lebanon and the PLO leadership wanted a base for their militias; the Lebanese state understandably didn't want a parallel state operating with militias within their borders; this lit the fuse on a country with an already fragile sectarian balance and dozens of sizeable minorities that had grief with the state and each other.