Personally, I think it's not related to the acting verb at all!
You use can when you mean you are able to, have the time or the will to, etc.
You use could when you were/would be able to, had/would have the time or will to, etc.
I can swim means I actually am able to swim.
I could swim means that I might swim if I felt like it, or trained, or had the time.
- For Teachers