I heard about this a few years ago and looked into it. It’s false. Starbucks never did anything like that.
Also, from the Starbucks website:
In fact, Starbucks has partnered with the American Red Cross and the United Service Organizations (USO) to provide coffee to relief efforts during times of conflict, donating more than 141,000 lbs of coffee and over one million 3-packs of Starbucks VIA.
Additionally, troops all over the world are enjoying Starbucks VIA Ready Brew in care packages they receive not only from Starbucks, but from their family and friends as well. In 2011, Starbucks provided over 220,000 3-packs of Starbucks VIA to the USO for their care package program.