There seems to be an over-expectation on the TRACKING features of the Facebook Pixel and Facebook reports in general. They are NOT supposed to track all conversions on your campaigns. FB reports are only tracking traffic and conversions from PAID impressions, not organic impressions!
Think about it in terms of Adwords: You wouldn't expect Adwords stats to show results from organic Google search. You need a different tool to track ALL traffic and conversions. With Google Adwords, of course there is its BFF, Google Analytics. That seems natural. But there is no such tool within Facebook.
So... use Google Analytics for that, too. All you need to do is use utm-tags in the URL tag field in your ads.