I would say... if there is a company with 6,000 employees... it's going to depend way less on the company and more on the team. Your direct manager, your teammates, the other teams you work with, the other managers involved... that can all wildly vary even within the same company.
They are fluid too. People come and go. Circumstances change.
I don't know how much top-down leadership effect really has. If the CEO + board of a 20,000 person company feel a certain ideology, is it really passed down 10 layers lower to managers working on small projects?