Well, you have already gotten to a second question. (That was fast.) If somebody says of someone, "She can't sing and dance" it tells me she can't do both at the same time. In fact, there is more that it doesn't say than what it does say. For example, it doesn't say if she can either sing or dance. (Maybe she can do both but just not at the same time.)
As for your original question, if a person doesn't speak clearly you can't tell if they spoke correctly or not. That's because you didn't understand what they said. So it doesn't make sense to say a person didn't speak clearly or correctly. You can only be sure of one or the other.