That would violate the terms of the agreement:

"If Assignee needs to assert any of the Patent claims against any entity for other than a Defensive Purpose, Assignees must obtain prior written permission from all of the Inventors without additional consideration or threat."

At which point whoever twitter was suing could claim that they had violated their own agreement so they don't have grounds to sue.

The agreement would likely be private, so as long as both parties keep their mouth shut about it (which they're incentivized to do), there is little risk for them.

Personally, I see this as a great potential bonus source of revenue for the inventor down the road, selling the right to use their patent offensively.

Most companies won't do it though, since it restricts the potential market for their patent IP, which decreases the value of their assets on their balance sheet.

The common law principle of privity of contract (see http://en.wikipedia.org/wiki/Privity_of_contract) means that contracts can only be enforced by the parties to that contract (although some jurisdictions have changed this with legislation). A defendant in a lawsuit against Twitter cannot assert an agreement between a third party and Twitter against Twitter.

Disclaimer: IANAL

As long as the inventor holds the patent, what stops them from making a new agreement with the assignee that allows non-defensive litigation?

Well, if this sort of agreement becomes widespread, it would effectively opt them in to being sued by other companies who have patents assigned under a similar contract. Also, it would be in breach of any other IPA contracts they've made with other inventors.

It's a neat concept. The more widespread these contracts become, the more litigation you expose yourself to for using your patents offensively.

The company still holds the patent, and can even sell it, but the inventor maintains veto control over its offensive use.

The top post in this very thread demonstrates how that protection can be easily bypassed.

No, it explains how the purchaser of the patent can get the inventor to go along with their offensive patent lawsuit, which is necessary BECAUSE the inventor maintains veto power. If that weren't the case, the inventor would have no say in the matter.

But what's the point of the "no consideration" bit? What's the point of two parties agreeing that they won't make a new deal later, when they can anyway?

They just have to say if pressed that there was no threat or other consideration, and that they agreed to let the other party use their patent offensively. Then collect their totally unrelated consulting fee.

Edit: Now I think I was wrong in this reply. I did not realize that paragraph 4 of the agreement gives the inventor the right to license the patent to another party to enforce the agreement. However, the broad language of the second paragraph still gives the assignee a lot of wiggle room to argue that they are not breaking any promises made.

--- Original comment:

I mentioned this in another thread, but it is actually simpler than that. As I read it, the twitter agreement gives all rights in the patent to the assignee, just like any other assignment, but it adds on the clause that the assignee agrees to get permission from the inventor if they want to sue offensively with the patent. In the future, if the assignee (whoever it is at that time) decides to sue offensively without the permission of the inventor, the assignee can (and indeed they have the right to, as the holder of all the rights in the patent). The inventor would then have a cause of action for breach of contract against the assignee, but who knows what that would amount to.

Basically, I doubt that a court would read the agreement in a way that prevents the future patent assignee from using the patent offensively, even without the agreement of the inventor.