Well, it wasn't as "Wild West" as DRG&W construction crews trading gunfire with AT&SF construction crews. By the turn of last century, things had gotten somewhat civilized (although the PRR and NYC&HR were still battling each other via tariffs). Out in the hinterlands, where the real work was done, everyone was on friendlier terms. Both roads had coal properties in the same area, and both realized there was only room enough for one railroad. Constructing a jointly-owned/operated railroad made sense. Yes, there was some minor horse trading involved, but overall it was essentially a clean deal. The PRR would build the line, and get reimbursed half. The NYC would maintain the line, and get reimbursed half. The NYC was better staffed to do the dispatching, so they did such, and got reimbursed half the cost. Both roads could operate over the line equally, and tonnage/car-mile costs were credited to the jointly-owned company (of which each had an equal share). Management swapped out yearly between the NYC and PRR. The "normal" switch alignment at Wandin (formerly Possum Glory Junction) also changed with the management change - under NYC rule the switch was normally aligned for the line to Heilwood (formerly Possum Glory), and under PRR rule the switch was normally alined for the line to Clymer.
The station building in Cherry Tree was interesting. It saw passenger service from both the PRR side and the NYC side (so it was technically a Union Station (don't know if it was ever referred to as such)). The depot was on PRR tracks, less than a quarter-mile from the NYC tracks, but the real estate for the depot was owned by the jointly-owned Cherry Tree & Dixonville RR, roughly a half-mile away.
I'm sure the bookkeeping was honest - there was no way any of the arrangement would have survived if someone tried cheating. Both sides could look at the books and conduct an audit.
Ex-NYNH&H SS Opr