Correct.
The rule is still "empty, clean and dry," but otherwise, yes, recycle those cans.
You can leave the labels on. If you opened it with a can opener and the top is detached, throw it in the trash and just recycle the can. The same goes if the lid is barely attached. If it is on solidly, push it into the can once it's clean.
What about those orange juice concentrate cans and coffee cans that are cardboard but have a metal rim? Don't recycle those, put them in the trash.
