A process is just a means, so a good process should start at the end.
Or maybe a better question; what do stakeholders want from us and what are the needed characteristics of the process to deliver that?
I said stakeholders because when you only do 'lean' things that add value for a 'real' customer, you will be broke and in jail in a week.
So outside in should indeed start with what customers want from you, but unfortunately more stakeholders are expecting something from the process or it's result.
For example, take Keith's red car. That's what customers want. And maybe they want if fast and cheap. So the process 'Deliver car' has to deliver this promise.
But the customer is not the only one:
The government wants that the process and car is compliant with a lot of rules on safety, environment etc
The factory owner wants a profit margin of 42% on each car
The employees want a safe work environment.
So, good luck my dear process to fulfill all these wishes.
So indeed outside in view is not wrong, but when you only focus on the customer, you might get disappointed in real life when the other stakeholders come in. So I would also take them into consideration.
And to me that's what inside out is about:
1. What result does the customer want (who is really paying our bills?)
2. What do we promise about that result (time, costs, quality, etc)
3. What do other stakeholders expect about the process or it's result?
4. What are the needed characteristics of the process to fulfill all these needs?