No, the inventors don't have the right to license the patents to whomever is being sued. 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). The inventor would then have a cause of action for breach of contract against the assignee, but who knows what that would amount to.
Did you actually read the agreement? Kliment is correct. The inventors are granted an irrevocable license to sub license the patent to any target of offensive use of the patent. IANAL, but presumably existing licenses on a patent are attached to the patent and are not just a contractual matter between the licensee and original patent owner.
You are right. The fourth paragraph does give some teeth to 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.
I don't see the nature of the teeth you refer to, unless everyone's making the assumption that all patent inventors are noble and cannot be convinced, at any price, to license their patents for evil purposes.
No, the inventors don't have the right to license the patents to whomever is being sued. 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). The inventor would then have a cause of action for breach of contract against the assignee, but who knows what that would amount to.