Are we producing value?

I read this discussion about using TDD/BDD in lean startups. They touch some really interesting topics there. Amongst others how TDD/BDD are great for client work but not so good for lean startups. Even though there is a lot of talk forth and back between client projects and lean startups I am confident that a lean startup is almost no different from  any other software project. Except for one significant difference Let me explain.

When working as a developer with a client we are focusing on delivering quality software meeting the customers demands. We have the integrity for our craft playing a role and we have our developer hat on. However and here comes the interesting part. When we're dealing with a lean startup we are actually wearing our stakeholder hat and our developer hat on. Because of wearing our stakeholder hat we are forced to think in terms of value or ROI.
This is the real difference. Not whether it's a client project or a startup. Or am I wrong? Is the client's stakeholder less interested in us producing high value than what we would want in our own startup? And why is being agile in our lean startup to succeed any different from together with the client stakeholder achieving success through an agile process? Whoever the stakeholder the project starts with a vision. A vision we will mold and change to in the end reach a valuable result.

If we state that TDD/BDD is a waste of time in our lean startup but not in our client project it sounds to me like we are stating that it's ok to waste our clients money but not our own. TDD/BDD is just an example here. I'm trying to put some light on our intents behind determining value. Are we loosing focus? Shouldn't we keep focus on constantly producing value at the highest rate possible regardless of the setting?

Am I way off here? What is your opinion?