At least at Google none of this is true. Finding a project that is visible and being a part of it will get you promoted. Being a go to person will get you a lot of pretty words about how great you are. Nothing else.
One place I worked had an informal piece of advice passed between employees: Either do something important well, or break something badly. If you don't you can't be noticed
It's a same thing everywhere. Hard work makes you a go-to person (at whatever). The go-to person gets you into high visibility projects. You ultimately can bargain your promotion using both of these qualities.
There was a guy I knew at Google who just went around figuring out what everyone was doing on a specific problem, made a bug for each one, and wrote a slide deck where he implied he was responsible for the cumulative result of 30 other teams. He's an L7 now.
I really regret telling him what I was working on.
Promotion at big orgs tends to be more of a game than anything else. Higher ups like empire building, and promotions (having higher level direct reports) increases their stature while also freeing up headcount at the now-vacant lower level slot(s) to grow their empire.
It’s not about what you do at all, it’s just about how you play the game. Many (most?) cases of positioning oneself for promo just involve casting a bigger shadow on the wall by doing the exact same work closer to the flashlight.
At L5+, if you are not playing the game you have very little chance of promo (you will have to work harder than any L+1 around), so if you are largely just interested in building and not posturing, you should just switch companies and make a diagonal move (and then, perhaps, come back).
This is also why you can’t do anything too risky (regardless of the potential reward) at Google unless you are capable of dishing out promotions - this game is what matters to Googlers, and things that don’t help with the game are efficiently discarded.
From the article: "I helped my first report at Google get promoted from Eng 1 to Eng 2 within 9 months, by advising her to find something that she can become the “the go-to person” for."