You could have asked me out yesterday. I know I was sick last week, but I was able to go out last night.

Try the same sentence with could have and the verb in the past participle

..., but I could've gone out last night. ( now I know that you didn't go out )

When she says she was "able to go out" I wonder if she went out or not but I still don't know for sure. 

It is hard to tell if Natalia went out last night or she just could have.