Post likes, shares and search history are all examples of data you've directly provided that they're omitting from the export.
As for your principles, when you ask the FBI for their file on you their obligation is not limited to data you've directly provided.
The FBI is subject to FOIA. FB is not, obviously.
It's in the Activity Log, which is omitted from the download. This is not obvious and misleading. In fact someone asked whether they could download their activity and Facebook directed them to the Downloaded Info, which omits it.[1]
As for FOIA, you're missing the point. Of course FB is not subject to such a law. The whole debate right now is whether it should be. If you request an organization's "file" on you, it should be comprehensive and not selectively omit the creepiest stuff.
[1] https://www.facebook.com/help/community/question/?id=6345563...
I would say no if before you signed up they were willing to tell you everything they "intend" to collect about once you agree.
And when I say "tell you" I mean an itemized list in plain simple english not a thousand pages of obfuscated legalese.
I would say if they provide everything you've directly provided, they've fulfilled their "obligation."
Obligation is in quotes, because I don't actually believe they should even be required to do this.