Nothing wrong with first thought-best thought, but to me that means the scene in general. It's how I present that scene that may not be right the first time around.
I think the teacher who said this was referring to word choice, but I've probably forgotten the context. Stephen King actually suggests something similar. He says, don't hunt around for a fancy word. Just use the word that comes to mind. I hunt around for fancy words sometimes, because I like it that way. But sometimes I default to this reasoning to keep my sanity.
I took writing classes in college where I was basically taught the opposite. Examine every single word to see if you can find a better one. I suppose there is room for all different schools of thought, but I think most writers are better off with a little bit of both.
I am a compulsive self-editor. I stop and edit a scene 3-4 times while writing it. Then I re-read it next time I sit down to write and tweak some more before writing the next. I frequently go back and re-read and tweak things. I wouldn't necessarily call this right or anything, but it's the only way I can write.
Some things I actively look for when editing:
Making nouns more specific. Changing soda to Pepsi or tree to Oak.
Making passive verbs active where it makes sense to do so. Changing she was walking, to, she walked. Also, more colorful verbs. She picked up the keys, would become, she grabbed the keys. She strolled, hurried, paced, etc.
Cutting out bland, unnecessary descriptors, like very, or, He felt that, etc.
Sentence variety. If I've written too many short sentences or long sentences together? Boring to read. I try to mix them up.
I think when we are just getting ideas down on paper, we default to repetitive phrasing and weak language. Our mind is focused on getting down the story, the images, and all that good stuff and if you stopped to check every word you would lose what you are trying to say. You just have to write down whatever comes to mind first because you are busy working out the story. In a first draft, those types of things make perfect sense. It's afterward that we can correct those things and make the whole more readable and interesting and vivid in the reader's mind.
I spent many years believing that I had to refine and perfect my prose to make it worthwhile. A book on writing by Annie Dillard made the whole writing process sound so painful that I almost gave it up! So, I've had to think a lot about this for myself. Editing is good stuff, but it should be a servant and not a master. Like all writing advice, take what works for you and discard the rest.