The prompt leaves the decision up to you. You can answer it however you feel like answering it. There isn't a right or wrong answer, but you absolutely must defend your choice.
Personally, I would argue that their social responsibility strategy is genuine because it creates a good public image. Starbucks is a for profit business. Their number one goal is going to be to make money. Of course their website isn't going to say that. It's hard to sell a customer a product, when that customer thinks the company only wants to make a buck off of them.
Being "green" is popular right now. Most companies claim that they are working to find ways to be environmentally responsible. Even oil companies do this. The following quote is from BP's website.
We prioritize the safety and reliability of our operations to protect the welfare of our workforce and the environment.
And here is the same kind of thing from Starbuck's website.
Our comprehensive approach to reducing our environmental impact means looking at all aspects of our business, how
they intersect and how we can integrate new solutions to create meaningful and sustained change.
As you can see, they are basically the same thing. They both emphasize protecting their business through protecting the environment. In fact, had I not stated which quote went to which company, you likely wouldn't know which statement went with each company.
For Starbucks, and most businesses, projecting a good company image to the public is good business. People will spend money at Starbucks because they like coffee. They feel better about their purchase, if they believe the company is a "good and moral" company. Starbucks is absolutely sincere in keeping its good public image, because it makes them more money.