Is Facebook Underestimating Engagement?

A couple days ago we wrote an article that did well on Facebook. Reach and engagement were much stronger than our typical post. As you can see above Facebook’s “insights” on the post show it reached over 40,000 people and had a lot of likes, comments and shares. It was almost viral with far more comments and likes on the shares than on the post itself.
We noticed, however, that the number of link clicks were fairly low. Less than 3000 people appeared to click on the link, and 8600 clicked on something on the post.
We noticed heavy traffic on our site in the last three days, nearly all for this one post about a restaurant inspection for a popular restaurant near our community.
So we checked. Jetpack Site Stats showed 30,000 page views coming from Facebook in the last week, a lot more than what our FB numbers suggest:

And our Google Analytics numbers also show a similar amount of Facebook traffic specifically to this page, roughly 30,000 again:

In other words, it appears that our site got 10 times as much traffic from this post than the “link clicks” number indicates, or more than triple the number of “post clicks”.
So, is Facebook underestimating engagement? Yes and no. Our best guess is that the link clicks shown in FB Insights is limited to clicks on the original post and does not include link clicks on the shares.
Still we find this suspicious. If our post was shared over 1800 times with all those likes and comments on the shares, and we got nearly 3000 link clicks just on our post, you’d think our total traffic would have been much larger.