CrowdTangle is able to pull in public posts from Pages and Groups on Facebook. However, Pages in particular have the concept of "targeting," where a post can be public but they choose for it only to be delivered to a certain segment of the population.
A clear example of this involves Pages representing alcohol; in the United States, the drinking age is 21, so users under 21 are not allowed to see those pages. They are targeted to users over 21.
Another example might be a sports team where broadcast rights within a particular country may be complicated, and users inside that country are not allowed to see the content because someone else owns those rights. That post is targeted to exclude users from that country.
If you see the globe symbol on a post, that post is public:
If, however, you see the gear, that post is targeted:
Unfortunately, if you want posts from a Page that uses targeting, chances are good that we won't be able to get those posts.