There is no explicit provision in the rules for forgoing that benefit. However, looking back to the definition of attacks of opportunity, we have this:
Sometimes a combatant in a melee lets her guard down or takes a reckless action. In this case, combatants near her can take advantage of her lapse in defense to attack her for free. These free attacks are called attacks of opportunity.
Avoiding attacks of opportunity takes effort. Provoking an attack of opportunity is something you do because you are forced to by the distracting nature of whatever you’re doing. That seems like a pretty solid case for saying that characters can always provoke attacks of opportunity, whatever they’re doing. The rules specifying that some actions provoke, in this argument, are really saying that while performing those actions, a character cannot help but provoke.
But this is definitely not something the rules come out and tell you. And even as I advocate for it being sensible to allow, I am a little worried that there might be some weird abusive corner-case to it. As GM, I would probably allow it, but with the caveat that I reserve the right to revisit that choice if it turns out to be problematic (as with any ruling ret-con like that, I would also allow players the opportunity to rebuild their characters somewhat in response).