To establish the existence of the limitation of action, I'll cite two cases from the Tipitaka, followed by argument from personal experience.
In the Samaññaphala Sutta (DN2), King Ajatasattu, who killed his father to gain power, learns from the Buddha and rejoices in what he learns. What the Buddha says afterwards is interesting.
So King Ajatasattu, delighting and rejoicing in the Blessed One's words, rose from his seat, bowed down to him, and — after circumambulating him — left. Not long after King Ajatasattu had left, the Blessed One addressed the monks: "The king is wounded, monks. The king is incapacitated. Had he not killed his father — that righteous man, that righteous king — the dustless, stainless Dhamma eye would have arisen to him as he sat in this very seat."
This suggests that Ajatasattu's fate (being killed by his own son, not being enlightened in that lifetime, being reborn in hell, etc.) was unavoidable, although if I remember correctly, the commentary said he was enlightened in the lifetime after his rebirth in hell.
In another case, there is Angulimala, who was a bandit who murdered many people, yet later became a bhikkhu and an Arahant. See the Angulimala Sutta (MN 86).
I believe Bhikkhu Pesala has taken these passages (among many others) to delineate in this article rebirth in hell, for various acts. Because, for instance, Ajatasattu killed his own father, his fate is said to be inevitable ("definitely" reborn in hell). But with Angulimala, he did not murder his parents or Arahants, so the potential for enlightenment was still there.
This is fairly logical analysis of scripture, but more to the point: What is it about these actions that makes their future effects mutable or immutable?
In our personal experience, there seems to be some kind of limitation to action, but it's a bit ambiguous. When we look outside of ourselves, we see a deterministic world, the mere shuffling of matter, but through introspection, we see a wonderful potential for freedom. People who misguidedly believe in either the extreme of determinism or indeterminism narrowmindedy focus on one or the other aspect of experience -- the internal or the external.
There is the feeling that over time, through my life, I have become this, yet now I have the potential to become something else. In Buddhist terms, in the past, the chains of dependent origination have caused this being to arise, which is old karma, but here and now, there is the potential to create new karma.
But to what degree is there such potential? It is hard to know. A person can overestimate their potential -- as if King Ajatasattu were to expect to not face the results of his actions -- and a person can underestimate their potential -- like Angulimala not expecting himself to have the potential for sainthood. One should not have unreasonable expectations.
The Buddha described Right Effort as tuning a stringed instrument, but a musical string can only play so many notes. The path is also described as taming a wild animal, but there are limitations there as well (can't teach an old dog new tricks?). Even when a person has, for the moment, had their mind set on new karma and right action, old karma still lingers and remains, in the form of nagging habitual thought-patterns which so often quickly re-emerge, laying the foundation for failure and doubt about the sincerity of the previous right intent. To maybe give more clarity to this question: At what point do sankharas become "right" instead of wrong, "new" instead of old, in the chains of dependent-origination?