These situations aren't really comparable. For one, Iginla was in a different era when the Flames were fighting to survive and they ended up giving him 20-25% of the team's payroll. The risk of the team leaving was high and they legitimately couldn't afford him. They buckled because they had to, losing Iginla would've been the last nail in the coffin. It was also a different CBA that afforded players more leverage, making it MORE likely that they get what they wanted. Not sure why you'd bring him up but Iginla sure didn't seem all that sad to leave at the end. He was probably exhausted after carrying the franchise on his back while management was constantly a decade behind the times, making poor decision after poor decision.
With Doughty, he actually ended up winning, so it's not surprising no bad blood was fostered. Doughty also wasn't an American kid playing in a Canadian city. Like it or not, it's more likely to be a factor than a Canadian kid playing in California.