You don't seem to use the common definition of a patent troll. Caltech very clearly is in the business of inventing real, new technology. You can disagree with their filing of infringement lawsuits, but they're not a troll in the way the typical NPE is.
I think you can be a "real" inventor in the sense that NPEs are not and still be in violation of the nominal intent of the patent system. Caltech is here. You can call that trolling or not; OP never claimed that Caltech was literally an NPE. It's absurd that parallel invention of similar techniques, without awareness or observation of the filed patent — which USPTO often grants for extremely trivial software constructions — puts you in violation.
It's especially absurd that 4x damages were awarded against Apple here when Apple is just a customer of the allegedly infringing party. 4/5 of Broadcom's customers were not assessed damages — why pick on Apple in particular? (I mean, we all know why — they have cash.)
It sounds to me like you're the one purposely changing the definition to discredit them. It's obvious from social cues that they're not using a strict legal definition.
I'm not trying to discredit them at all. I think the question of patents and trolls is a very important one. It's worth making sure we are not confusing the seriously awful behavior of patent trolls _exploiting_ the system with the intended functioning of the system.
(We can have a rousing debate about whether the intended functioning is something we think is societally advantageous or not, but the changes to that are different than the fixes we need to prevent patent trolls from causing so much harm.)
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