tl;dr Not ever. Skills FoRK into [opened] skills only.
Taelor’s post from another thread hints at the problem:
Unfortunately, earlier editions often used FoRK as a general term for adding dice to a test when it really should have said advantage. I think the chase section there was the only place not changed in BWG.
Also note that Beginner’s Luck tests are stat tests, not skill tests. No FoRKing there, either.
My rule of thumb is you should never try to infer a general rule from a specific rule.
Thanks for highlighting this again. It was me who raised the question in the previous post you’re referring too. Searching through the forums it does seem to be a bit of a confusing thing. As you say the book makes it clear most of the time that Forks are a skill only thing yet some people give examples of Forking into stats sometimes. As someone else pointed out it’s not that big a deal…you’re not always gonna have situations where you have a skill relevant to fork into a stat anyway but I think it’s good ot have it nicely ironed out.
BTW, recently, while reading up on the special rules for dwarves, I noticed another instance of non-skill-FoRKS – the Greed section talks about FoRKing Greed into Circles. (Technically, both are not stats, but still.)