You can know things that aren't
true. Knowing something does not explicitly imply that those things are true or
false or anything in between. If he had said, "I know some things that are proveably true", then that's kind of questionable depending on what
assumptions you have to begin with.
The act of knowing and the idea of knowledge does not forceably imply truth. Knowledge is formed of all kinds of things from opinions to facts to history to math to experience. Very little of that is mathematically proveably true.
So the statement "I know something" is absolutely true. The statement itself is a piece of knowledge and having one piece is something.