I think you’re in the right neighborhood, but I’d modify it somewhat: Bin Laden was trying to convince a global audience that his cause was righteous and true and blah blah blah, and much of what he said was wrong or self-serving. Then there’s the whole mass murderer thing. So you can’t take him at face value uncritically and it’s true he was self-aggrandizing in the extreme. But that doesn’t mean you can ignore what he says about what he’s doing and make up new motives out of whole cloth and then say you know what he’s after. “They hate us for our freedoms” is pretty much exactly that, and saying it’s 50-50 between U.S. foreign policy and U.S. culture is not that wrong, but near it.
The whole point of terrorism is to scare people into doing what you want. If you don’t tell them what you want, it doesn’t work. So Bin Laden did say what he wanted and why he was doing it. The stuff surrounding that - we only want to help Muslims, our struggle is justified, we’re being oppressed, we’re going to win - is all bullshit. But if you say that Bin Laden’s own comments about what he was doing and why can be ignored and replaced with a bunch of generic pap about how he hated American culture because it’s just so great, then what you’re saying is that Osama Bin Laden didn’t know the first thing about terrorism.