It has been known for a while that there are issues in Sitecore 8.0/8.1 with the field level fallback when using template inheritance (which everybody should use!). For the above versions Sitecore created a support hotfix with the number 105327. This blog post is outlining the issue in more details.
It turns out this issue is still present in Sitecore 8.2 but unfortunately the aforementioned hotfix no longer works for 8.2. I reached out to Sitecore support and they have created a new hotfix that works for 8.2 with the number 184934. You can download it from here if you want it without having to request it from Sitecore support.
I hope this helps for people who need the language fallback to work in more advanced setups.