Company, Team, Self is backward, but not in the way you think. It's backward because it's advice given to employees, when it needs to be given to be given to management. Employees will and should do self-interest. It's the EXECUTIVES's duty/problem to ensure that they make workers' self-interests clearly aligned with Customers/ Company/Team/Self. It's an interesting exercise to consider how to make it in an employee'…
There is no way for executives to create a well working company if the employees think of nothing but themselves.
If I put the company and then the team first, and the team and company think the same way, who is there to look out for me?
Only a sociopath, and a stupid one, would put their company ahead of their family. And there aren't that many sociopaths in society.
Loyalty must be earned, and most companies have earned not loyalty, but resentment and deep distrust.
(I have been lucky that I have mostly avoided such companies, because I have a fairly rare talent, but not entirely. Oh, boy.)