Xanderous, there are a million books out there on how best to write fiction, and that one is the only one I've ever encountered that was worth a darn. On Writing is a fabulous book and you should generally default to trusting what he has to say in it. His point about dialogue tags is principally that you're trying to make the reader forget he is reading. It's like great direction in a movie: A bad director causes you to notice his artsy camera angles and musical choices and in the process distracts you from the actual story. You're constantly reminded that you're watching a movie, so you can never lose yourself in it. A good director doesn't have to be a genius of the art; he can just be good enough in a workmanlike way that his direction doesn't get in the way of the story. If you forget that you're watching a movie and just watch it, he has succeeded far more than any number of aspiring artsy-farts directors (or see Tony Scott's early work compared to his frenetic later movies). The true geniuses are the directors who can be artsy, but in a way that enhances our viewing experience while we never quite actually notice it at the time--at least during the first viewing. The unique camera angles, the experimental framing, the slow-mo bits, are there, and in the moment they just work, heightening the movie above what a workman director would create without distracting you from it.
Stephen King is talking about that with writing. You don't have to go purple. Far from it. You don't even have to get fancy. If the story itself is engaging enough that your readers get in the groove, their brains won't even process the dialogue tags in a verbal way. They'll purely subconsciously register them as tags, just enough to keep track of who is saying which lines, without actually reading them as part of the writing. And that's fine, because during dialogue, it's the dialogue that's telling the story, and you want your audience to lose themselves in just listening to the conversation in their heads. If you try to get fancy with stuff that's not the dialogue itself, you risk reminding them that they're reading, taking them out of the moment. Some people can be fancy without being distracting. The geniuses. The rest of us? We are well advised to let the story be the star, not the writer.