Well, the majority of the time, CIS is just a particularly, if contradictory and paradoxical, high showing for the character in question, with the real problem being that, basically, everybody is wearing rose-colored glasses. They see only the feats that they wish to see, and they blindly pass by and blithely ignore what constitutes a low showing for the character in question. Sure, the character fluctuates, but there is something of a middle ground, which does not have to be, in all actuality, the character's actual profile. The mercuriality and flux of any character that has not been exclusively written for is assured, and even when you have a singular writer, there is still the off-chance that he attempts to raze and wreck what he has built up. A character could, one day, have trouble with ordinary street thugs and insane asylum patients, and the next day, go toe-to-toe with gods, demons, unspeakable horrors from before the dawn of time, scientific aberrations that have destroyed terrestrial spheres, fallen celestial beings, and in general, horrors that the character should not even begin to be able to want to quantify the smallest imaginings of tackling. Of course, there are certain incidences where you get unimaginably poor writing, that goes against everything that the character is and has ever been, and that, IMO, is true CIS.
PIS is a different mechanism used by writers, though. It is merely a vehicle by which means the writer in question can transport an act of God into the storyline, and by that means preserve the character from whatever harm he comes in contact with, creating extraordinary bouts of luck and unbelievable exploits that defy whatever sense of logic and common sense the reader might have. You could have an ordinary, everyday human with no abilities that are out-of-place in this world, stroll through sustained gunfire, survive falls that should shatter their body and leave them a crippled husk, preform acts of puissance that rival that of the powers that be, and in general proceed in such a fashion that offends the sensibilities of anyone who expected to read a mature story, and instead received an anticlimactic fairytale, where everything has been said and done, and all that's left is to flip the pages for surprises that you expected and twists that you saw coming to jump out at you, but all in a way that furthers the tired, worn, fatigued plot. By means of this particular form of plot, the writer can basically trash the story, turning it from an adventure, into a completely clichéd romp through the park, complete with commonplace occurrences such as megalomaniacal villains attempting to conquer/destroy the world, all in the name of good triumphing over evil.
So, to answer your question, CIS is possibly acceptable, as long as it is not too incredible, as at that point, it ceases to be that character, and instead, becomes an entirely different thing altogether. PIS is not really acceptable in a debate, as it is nothing but plot device, put in there so that the hero triumphs despite, literally, impossible odds.