Oak as a trainer. (Sammy Oak)
No Oak doesn't lie. When he was a trainer he travelled just like Ash.
He appears as a young boy, Sam (Japanese: ユキナリ Yukinari) in the fourth film, Celebi: Voice of the Forest. Ash Ketchum befriends the young Oak, who, because he time-traveled from 40 years in the past, is around the same age as Ash. The revelation that Sam is Oak, while inferable thanks to disclosure of Oak's first name in The Power of One, comes only at the end of the movie when Oak impliedly confirms the connection through his knowledge of Sam's name despite Ash having never told him of it. Additionally, Tracey finds the sketchbook in which young Sam drew Pikachu sleeping with Celebi in Oak's closet. ~Bulbapedia
To read up more about Oaks journey in Johto check that link under "Past".
So yeah, Oak has travelled to Jotho