That is not true at all. Prior to the modern playoff system lots of players on non-winning teams won MVP Awards. (I assume you mean non winnig as in “didn’t make the playoffs.” Cal Ripken, Dawson, Ernie Banks twice, Keith Hernandez sort of, Mike Schmidt in 1986, Burroughs, Jim Rice, Bobby Shantz, Yogi Berra in 1954, Willie Mays in 1965, Orlando Cepeda, and on and on.
First of all, Babe Ruth never won the modern incarnation of the MVP Award. The Award as it currently exists was created in 1931.
Almost all of the worst MVP choices of all time were relief pitchers. Choosing a guy who pitched 80 innings, like Dennis Eckersley in 1992, is simply insane. Eckersley would not have been the MVP if he literally had not given up a single run. Even prior to that when relief pitchers pitched more, like Willie Hernandez in 1984, it was a crazy choice. Willie had a hell of a year but he was not the most valuable player on his own team. So there’s four bad choices; Konstanty, Fingers, Hernandez, and Eckersley.
Once you get past that, you can find a lot of silly choices picked because they guy drove in a lot of runs, even if he wasn’t all that good at anything else.
This is a phenomenon that has happened throughout baseball history. Hank Sauer in 1952 was a preposterous selection. He led the league in homers and RBI but he was a slug of an outfielder on a 77-77 team. Andre Dawson in 1987 led the league in homers and RBI and did nothing else well, and his team finished dead last; he wasn’t one of the ten best outfielders in the league. The same year they gave AL MVP to George Bell, who was better than Andre Dawson but who really should have sent his award to Alan Trammell. Awhile after that they gave an MVP Award to Justin Morneau because… honestly I am not sure why. He had a good year in 2006 but an OK defensive first baseman who doesn’t lead the league in any offensive category does not scream “MVP” to me. Derek Jeter, who finished a close second, was a clearly superior choice, and so were some other guys. Other examples of the RBI Guy winning over a way better player (not a slightly better player) would be Jackie Jensen in 1958, Jeff Burroughs in 1974, or Don Baylor in 1979. Juan Gonzalez in 1996 was a ridiculous selection, probably as bad as any in MVP history.
I should point out, incidentally, that I am actually being more generous ion my definition of a bad selection than some people who have posted before me. I agree Don Mattingly was a poor choice in 1985 - Rickey Henderson or George Brett were much better picks. But he wasn’t AS bad a choice as some of my examples, certainly being a way better player than the likes of Hank Sauer, and in 1985 the BBWAA’s understanding of how baseball players should be judged was not what it is today. Mattingly’s selection is not a really bad pick the way Dawson or Bell were two years later. I’m also unwilling to assume WAR is always right, because it simply isn’t, and especially in the past small differences shouldn’t be made much of; BBREF says Mickey Mantle was 0.6 WAR better than Nellie Fox in 1959, but no one can look you in the eye and tell you honestly that they are SURE Mickey Mantle had a better year than Fox based on that metric being retroactively applied to 1959. 0.6 WAR is a very small margin.
I’d also shrug at anything REALLY far back, like Frankie Frisch in 1932 or Ernie Lombardi in 1938. This was a time when just knowing how many walks a guy had was not easy information to get - the year Frankie Frisch won the MVP AWard, they didn’t even count the number of times you were caught stealing. They certainly had no understanding of things like park factors, and our true understanding of the defensive abilities of guys in that era is not, in my opinion, reliable on a year to year basis.