He wanted out long before the playoffs last year, and that didn't change this summer. This idea that management just assumed they could offer whatever and he would take it is silly. Like they have no finger on the pulse of their own players and don't actually talk to them behind the curtains.
I'm sure they were well aware of risks involving Broberg being offersheeted and didn't think he would just sign whatever they wanted to throw at him.
They did offer Broberg something though, and my assumption is reasonable based on what was offered.
You also have no better idea about what Broberg thought of the team than anyone else. Yes he requested trades, but the reasons for doing so are more complex than just that he disliked the organization
All signs point to that he was displeased because he wasn't getting NHL time and opportunity. It didn't seem to be about money. That is another assumption but that's the best assumption based on the info given
So yes, it does seem that the Oilers were a bit arrogant by assuming that Broberg would be appeased by telling that he was guaranteed a spot on the team this time having earned it with his excellent play in the playoffs, and likely top 4 as well.
And again, we are all in the dark on this one for the most part. To me this narrative is the one that makes the most sense. Either way it's just splitting hairs. The Oilers misread and mismanaged the situation in some way. The final outcome is proof enough of that