By claim, I suppose you mean sue over? In that case the answer is no. There's this notion that companies legally have to be run so as to maximize shareholder value, and there's some case law in Delaware to support that notion. But what overlooked is the context of those decisions. Invariably the litigation has to do with change of control or measures designed to encourage/discourage same. Outside of those contexts, the business judgment rule reigns supreme. So long as there's no self dealing and the company doesn't lie in its public statements, it is almost impossible for a shareholder to win a derivative breach of fiduciary duty case.
Corporate officers have wide latitude in determining what actions are in the best interest of the corporation.
In a case like this, the incentive to initiate Nuclear Armageddon for profit has to be balanced against the cost of making developers hate you and desecrating your reputation and standing in the community. It is by no means clear that starting a war in which all sides are susceptible to take heavy losses will be in the interest of shareholders.
Patents are a weapon, and if one huge corporation has no "weapons" to defend itself with, then others with "weapons" will attack it. That's why they all have to participate.
In this case, they all - Google included - rushed towards a particularly juicy weapons cache, and whoever got their hands on it was going to use it on the others.
This is fucking ridiculous and disgusting, of course. But it's not the fault of these corporations - they're forced to play, because if one doesn't, then others will just force a massive competitive disadvantage on it. The real problem is the US patent system, the US courts, and the culture of feverish bullshit litigation at every turn that pervades the US.
Note: I am certainly not arguing that this is a good thing for anyone by any means at all.