Would it surprise you to learn that Harvard does not have it quite right when it comes to teaching people how to lead a startup?

To be fair, Harvard's leadership courses are on the right track. But in the real world, the CEO of a rapidly growing beauty supplies technology company told me that she found herself adjusting Harvard's lessons, sometimes in surprising ways.

But a Harvard-educated professor of leadership in my department at Babson College thinks this CEO's leadership ideas may work well for her but also might be over-simplified and would not apply to everyone.

The dialectic between the young CEO and the leadership professor strikes me as thought provoking.

The CEO in question ought to know. After all, Leah Ashley of Color Me, "a leader in sonic makeup application," has a Harvard education with all the trimmings. She earned an undergraduate degree in economics, worked as a consultant at Bain and in private equity, followed by an MBA from Harvard Business School (HBS) and three years as director of beauty partnerships at Birchbox.

The professor is Allan Cohen, Edward A. Madden Distinguished Professor of Global Leadership at Babson College and the holder of an MBA and DBA from Harvard.

Last fall, with help from her business partner, Eric Jimenez, Ashley launched Color Me's 54 sonic makeup application, an automatic sponge that pulsates nearly 15,000 times per minute to mimic rapid finger tapping. Industry experts expect ColorMe to hit $15 million to $20 million in sales, according to WWD.

Here are her six leadership lessons, how she has tweaked them since HBS and what Cohen thinks of some of them.

1. Inspiration should move employees to serve customers better than the competition.

Leaders are supposed to inspire people. But if Ashley inspires her partners and her team, it is because her customers give her inspiration.

Explained Ashley, "I let customers lead me. I stay close to them through focus groups, surveys, and customer reviews. And I convey their values clearly to my team. Customers want us to make them feel confident that they can apply their makeup quickly, that it will look good, and last all day."

Cohen thinks there is more to a good vision than customers. As he said, "While I agree with taking inspiration from customers, what particular inspiration, how it fits with market needs/potential profitability, capabilities to deliver it, are important. Arriving at a viable and inspiring vision that can move organizational members isn’t so easy. I do agree that having a fancy vision doesn't mean much if you can't execute on it, but it sounds as if she underestimates how hard it is to get one. The combination she has arrived at sounds like it is working for her, which is great, but not necessarily easily generalizable."

2. Vision is nice, but results matter more.

Leaders are also supposed to have vision. But vision seems over-rated when 99 percent of success has to do with disciplined execution of what is hopefully the right vision.

Ashley explained, "People talk about how leaders must be visionaries. But it's all about results and execution. Vision is still important. I am leading a sonic application movement. When people see the product, they are blown away, they become true believers."

Vision only takes you so far. "I focus on numbers; the number of women who apply makeup, the number of distribution points for our product and picking the right ones, and operational numbers like how much it will cost to design and distribute a new product and how big we will need to be to gain economies of scale in making it," Ashley said.

3. Low tech can be better than high-tech.

With everyone glued to their smartphones as they barrel down the street, you would think that business success depends on smart technology. But Ashley rejects that idea. Instead, she believes that the most important communication must be face-to-face. Some technology helps with that, other technology is an impediment.

She sees problems with email. According to Ashley, "Email can easily get ignored if you have a flooded inbox. How can you tell what is urgent? And the meaning of emails that you do read might be lost in translation."

Direct communication is better. Said Ashley, "My cofounder is always on the road and I find it best to hop on the phone, on Skype or Facetime."

4. Listening is more important than talking.

Harvard sort of teaches this one. It has an idea "advocacy and inquiry" which implies that a leader must make her case and then ask questions to make sure that people buy in.

But Ashley learns more from listening. "I ask questions of our partners and listen to what they say and what they don't say. For example, when we talked with QVC about featuring our product, they did not initially ask about the personality of who would present our product. I realized that [Color Me cofounder] Eric had the vibrant personality that would be perfect," she said.

5. You can't do it all yourself.

To be fair to HBS, building a startup team is something the school teaches. The key is figuring out all the skills that the startup will need to be successful and to make sure that the founding team excels in them.

For Color Me, those skills are product innovation and managing the operations. "Eric and I complement each other perfectly. As an internationally known makeup artist, he understands what women want in makeup application and can develop better ways to do it. And I bring the ability to form partnerships and manage the operations of the business."

6. Leadership gets more complex as a startup grows.

HBS puts a lot of emphasis on leadership but do students really need to read the thousands of pages that have been written about it? For Ashley, it's all about treating others the way she would want a leader to treat her. "I treat my team with respect. I recognize their talents and accomplishments. And I thank them for it," she said.

Cohen thinks this kind of leadership is more complicated. "Leading the way you want to be led could well be effective, as long as people you are leading are like you in terms of what they want, and your experiences aren't so idiosyncratic that they wouldn't speak to others. Furthermore, leadership is all intertwined with the actual business, even though because of the nature of the English language we talk about it as if it were separate. You can have a wonderful leadership style in terms of interaction, but if you're making bad decisions about strategy, marketing, operations and so on, it won't matter much," explained Cohen.

Moreover, Cohen seems to anticipate that Ashley will find leadership becoming more complex as ColorMe grows. As he said, "An early stage startup, where interactions are face-to-face, often in a small space, leadership has fewer of the complexities of larger organizations, where communications are more easily distorted (although even two people talking directly can manage to distort things pretty well!), Groups start to become silos with separate objectives and agendas, people lose sight of the vision and strategy."

I think there is much that startups can gain by considering Ashley's six principles and the broader context in which Cohen places them..