The problem with the Edmonton offer sheet from their perspective was that they were not in the position to offer it. The Oilers were coming off a poor season, finishing 11th in the Western Conference. They had just traded their "heart and soul" in Ryan Smyth for a number of prospects and draft picks and had seemingly committed to rebuilding. Then they spent over $4 million dollars a year on Dustin Penner, losing 3 draft picks in the following draft. Strange. Now the Oilers have a weird amalgamation of good young players, overpaid free agents, and aging goaltenders that no one likes. They might make the playoffs but they're not likely to be a favorite at any point in the future and the money given to Penner can't be used on anyone else. The Oilers are a strange team.
The Ducks, on the other hand, were precisely the kind of team that was in a position to poach another team with an offer sheet. The problem, of course, was that they didn't have any money.* The Ducks ended up getting screwed by a problem mostly of their own making because for some weird reason they had signed Todd Bertuzzi and they lost Dustin Penner. This ended up killing them last season because what position did they need to fill the most? 2nd-line left wing, the exact position Penner filled last season. You may wonder why Penner is perfect in this spot yet subpar for the Oilers. One, stop asking questions. Two, when Penner was playing with Getzlaf and Perry he didn't have to bang in the corners (because Getzlaf does that) and he didn't have to fight in front of the net and paw at defenders like a little bitch (because Perry does that). What he could do was hover and find the open space for a Getzlaf pass, and he does that pretty well. Bobby Ryan will most likely fill that position in the future, but by that time Scott Niedermayer and Teemu Selanne will be retired and the Ducks' Stanley Cup window will have temporarily closed. Hooray!
*That's why offer sheets aren't more popular, despite all the hand-wringing by writers and GMs: the teams that would benefit from them are good teams that want one more piece, but those teams are generally near the cap; the teams that can afford to spend the money need the draft picks to rebuild their franchise.
Of course, creating a counterfactual where Dustin Penner stayed on the Ducks creates a whole other set of scenarios: they probably don't sign Mathieu Schneider and they probably trade Andy MacDonald anyway. Maybe they end up trading Penner anyway and get less than the 1st, 2nd, and 3rd round pick they got for him. But overall, I think both teams screwed themselves: the Oilers ended up with an overpaid player that doesn't fit their needs and the Ducks were hurt in one of their last years at being competitive for a Stanley Cup. It's pretty awesome if you think about it. You know, for me. The Oilers are one of those teams that could contend for a few years if they got their act together and I hate the Ducks, and in one fell swoop they managed to destroy each other. Now I just need Erik Johnson to get hurt and the Blackhawks to waste all their cap space on a red-headed goof and the Kings should be all set in the Pacific. Oh wait, that happened? Excellent. *strokes white cat