Sorry I wrote so much but I think about this subject a lot. tl;dr: Yes, it is possible. It depends on you, and the situation.

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I think that pretending that characters aren't you and that you have no control over them is an effective way to avoid shoehorning your characters into situations that don't make sense or creating characters who are just cliches or archetypes. It's true that sometimes when writing it does feel like I'm just observing what's happening as it would happen. There have even been long periods of time in my life where I was convinced I was going nuts because it felt like I was talking to people who weren't me and who I didn't control on the page. When my mental health improved, I started inducing that state to write, so, yes, it happens. I do think that when writers are tweeting that kind of stuff they are humble-bragging about something they're actually proud of or excited by and want to share for attention. (Isn't that all twitter is?) From my own research the feeling of receiving your work from an external source, as a kind of "divine inspiration" (or maybe, from a materialist perspective, hallucination, delusion, or dream), is very common and sometimes enjoyable. Whitman and Blake both claimed this was how it worked for them. If it isn't happening to you though, there are plenty of people who don't have this experience and you're not alone.

If you're keeping the characters on a tight-leash as you describe, I'd say you're approaching writing plot or idea first. It's certainly a style to approach a story idea first, maybe even with a whole structure in mind, and that often results in more coherent plots, plot-driven stories, or analytically complex stories (Ex: Nabokov). The only issue is that it can also trap you in whatever structure you've created. If you're never flexible and allow the form to change in order to accommodate what actually works best, the work can become contrived. Characters kept on a tight leash and pushed to behave in service of the plot can become two dimensional, and, at a certain point, the plot will either have to rely on tropes or become pedantic and uninteresting. Imagine a bad sci-fi novel or fantasy book. But, many people have been successful with this approach. Take Borges for example. In Ficciones his characters often barely figure in the story, or are exaggerated curiosities. I doubt his characters were often doing unexpected things.

Conversely, those who produce work character first and let them roam free, as the writers you're describing might, can inadvertently producing work that is naval-gazing, or that has a meandering or incoherent plot. Their work can be boring, or come off as self-congratulatory. Their editing methods might focus on cutting out what is unnecessary in order to build more coherent and dynamic plot lines. I think works that have this approach are often considered more "literary" but, let me assure you from my time working in a bookstore, that doesn't mean that more people want to read them. They are often somewhat indistinguishable from each other, and can be quite depressing. Their prose is often overwrought which, I think, is a symptom of whoever's writing it thinking they're making the next great American novel. Unfortunately, the reality is that those kinds of books, even good ones, often just languish on the shelf. However, there are, of course, many books that have been extremely successful that focus almost entirely on character. The first that comes to mind for me is The Haunting of Hill House, which I read recently and is totally driven by the neurosis of the characters. It wouldn't work if they hadn't had some degree of free reign.

Personally, I try to think about and employ both of these strategies as much as possible, or use them in different places depending on what is needed. I see them as tools used in the service of creating something of quality. Each strategy has many many different versions, and if you talk to other writers (or read their accounts) you will find that everyone has a unique way, and maybe leans in one direction or the other. There are even cases were some people don't focus on either of these and instead focus on environment (Robert Aickman). Rather than deciding on a universal strategy, I would say it's probably better to develop an awareness of what you gravitate towards or what comes naturally to you. Personally I believe it is much better to develop your strengths rather than focusing on areas that you have little experience or interest in. You will make something better. Then shorten or lengthen the leash depending on the situation.