Yeah, it’s true. The only counterexample I can think of, since the modern primary process was put in place, is in 1980 when Reagan chose Bush, his main rival in the primaries that year.
However, there’s an interesting countervailing force at play. Among prominent Democrats who would make a good running mate, are there even any out there who aren’t already running for president? That being the case, there could be a “last two standing” effect, possibly. (Though if Biden gets edged out, as I expect to happen eventually, he’s of course not going to accept the VP role a second time!)
