I'm interested if that is true for players that are shifted. Looking at McCann's shift stats with men on base he has a 129 wRC+ as opposed to a 101 wRC+ (career averages).
I know that doesn't necessarily negate your argument, but I think there are certain players that benefit from having men on base. If the Braves are getting on base at a higher rate then the average team then perhaps they will be more prone to cluster luck.
I went back and look from 2010 till now. League average with no runners on was between 93 and 96 wRC+. With runners on, it was 97-101. Significant jump in OPS and a little increase in BABIP. So, I guess on average players do hit better with runners on base. However, that doesn't mean the Braves have been less lucky bc on average teams hit better.