If owners had a measure of control of how their teams performed in 1-run games, then I would expect to see the same owners having good 1-run records year after year, league after league. I don't have the data handy, but I would be shocked if this were true. My 1-run game record has historically been bad. I don't think I drafted this year's teams with any different strategy than I normally do and I had the best 1-run record in the tournament this year. I will admit that I was very lucky.
While I will agree that 1-run game winning% is not pure luck, it's way more luck than skill. If I recall, Bill James devoted an entire chapter to this in one of his early Baseball Abstracts. When I first read this, I remember thinking this was crazy. Good teams have better relievers and should win more 1-run games than bad teams, but Bill James' had all sorts of data that proved the opposite was true.