As I said, no, I don't think one automatically goes with the other. Being a good actor takes a lot more than just being able to tell a good lie or to convince people of something. Becoming a character convincingly is taking on another skin. You're not "you," you become someone else. You react as they would react. A good trial lawyer only need to present information as fact and do so strongly enough, with enough authority to present a reasonable doubt. That's not acting. Throw enough convincing facts at people and you'll get them to believe you. Melvin Belli may have been able to convince a room full of people a killer was innocent, but that does not mean for a moment he could convincingly portray a character in a play or movie. At all. He can just win an argument because he feels his case is strong enough and he believes in his point of view.
There is a lot more to acting that that.