I agree with this.
Only if the player is made an enemy of the BoS through either killing members or assisting the Institute in the quest Mass Fusion do the BoS turn on the Minutemen, because they consider the leading member of the organization an enemy.
If you succeed in destroying the Institute with the Minutemen while the Railroad and the BoS still live, both organizations congratulate you on your victory, though the BoS grumbles about not getting to do it.
Do note that is not what is going to happen lorewise. The RR wants to destroy the BOS for killing synths and the BOS wants to destroy the RR both to defend itself and because they can help synths escape.
You are only delaying the inevitable. The BOS knows where RR HQ is. Eventually, the BOS and RR are going to come to blows. The fact that PAM gives you quests to kill BOS patrols even in the MM ending proves this. In other words, they aren't working together.
Glad to help. Hopefully you enjoy the rest of your playthrough. Have fun, and remembers -- it's your game.
As long as you don't do any of PAM's quests (or really even talk to her), the BoS and RR within the framework of the game don't commit enough resources to each other to come to open war. The RR is too busy with the huge influx of synths from the destruction of the institute and the BoS has re-oriented its focus far too heavily on vertibird patrols to destroy raider, supermutant, and feral ghoul concentrations.
At least, that's what my head canon says. You're free to disagree (or do the quests), as always.