Skyrim is definitely not an RPG since your character's personality is inexistent and irrelevant.
Another point I don't get (well, beyond bashing a popular franchise, but many people make the argument regardless of that). Take Planescape Torment as an example, a game routinely praised as a RPG. I can run in circles in the main square like I'm mentally challenged for minutes, and then I can murder one of my companions for no reason, and right after that I can have a conversation with a bystander, who will fail to mention the brutal, senseless murder that occured right in front of him, and my character who by all appearances seems like a complete lunatic will have a coherent conversation in which he will outwit that onlooker, because my intelligence stat is 20.
Sure, you can handwave this away with some imagination. Maybe the bystander is scared shitless and tries to pretend nothing happened. Maybe my Nameless One has temporary fits of insanity. You can handwave just about anything, in Planescape Torment as in Skyrim.
I don't have the extensive experience people who seem to hate the latter game have (masochism?), so I haven't killed the Emperor nor ran into some of the nonsensical scenarios mentioned as examples, but my own Dragonborn is so far consistent as a no-nonsense woman forced to go along with a destiny she didn't ask nor care for. She's turning down quests she deems morally wrong and tries to stick as close as possible to her moral code when she's tricked into stuff she'd rather not do, and that's the end of it. Kind of like how people behave in real life, as everything isn't sunshine and stars aligning perfectly to give you the story you wish you'd live. That's roleplaying to me - playing a character in a world, rather than playing a character in a vacuum.
About the weirdest thing that happened was an assassin carrying me on her back to a random hut dozens of miles away while I was taking a 1 hour nap in hidden dwarven ruins. Perhaps this is where the argument comes from, perhaps you feel the system itself is designed to be inconsistent at times. But again, it's not hard to find justifications. Perhaps the assassin followed my character around for hours before she got into the ruins. Perhaps she drugged my food while stopping at an earlier inn. Just because *I* know that mechanically there was no one behind my character and it's just a scripted event triggering because I slept at a particular point in a quest line, just because there's not a giant flashing sign in my inventory saying "this apple has obviously been injected with some sort of sleeping drug", does not ruin the story, unless you want it to be ruined.
Besides, where is the line in a consistent system vs an inconsistent one, even if we exclude the player? Bystanders staying indefinitely, without moving or eating or sleeping at one spot is accepted in most games (save for, ironically, the Elder Scrolls). NPCs endlessly repeating the same lines of dialogue, or closing off their dialogue choices past a certain point, are also common.
For now there's not many ways around that unless you make your game completely on rails. It doesn't affect my own game one bit if xX_joe_elite_gamer_Xx decides to kill the emperor and wear his skin as a mask while leading the imperial troops to a charge against dragons, because none of these things happened in my game universe. So there is the possibility to do that - so what? I'm not a child. I don't have to be the archmagi and also get in bed with magic-hating Nords if I don't want to, just like I don't need to bunnyhop like I'm high on sugar if I'm trying to have an immersive experience playing a zombie FPS. Trying to push a game to its limits, to purposefully take various and specific steps to see how the system responds can be a fun experience in itself, but at this point you're not roleplaying, you're metagaming. In the end any system giving you a sufficient degree of freedom can be broken. If you make it a point to behave out of character, you'll get your wish.
Of course I'm not going to defend Skyrim as some magnum opus of the RPG genre. But to me it is definitely a RPG. Arguably a mediocre one, perhaps, but a RPG nonetheless.