Two examples from Into the Wild that connects to Thoreau's quote based on Chris McCandless.
"If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. It is not important that he should mature as soon as an apple tree or an Oak. Shall he turn his spring into summer?"
Thoreau's quote is all about somebody refusing to be a sheep and following the rest of society just because that is what he sees everybody else doing. Thoreau urges his readers to walk to the beat "of a different drummer" and forge their own path in life, often going against society and the expectations of those around us.
If we think about this meaning, we can clearly see that this is what Chris McCandless did in so many ways in his life. For example, even at school, in spite of being very intelligent and so gifted, he received an F in Physics once. Chris received this low grade because he refused to follow instructions and insisted on doing his own thing in writing a physics report in his own way instead of following a set format specified by his Physics teacher. Even at this age he did not conform easily.
The second example could be the way that Chris, in spite of achieving his degree, then went on and gave away his savings and lived the life of an itinerant labourer rather than trying to get a job and entering the rat race. This of course caused his parents to worry about him a great deal. The fact that a son who had shown so much promise then would seemingly throw away all of his opportunities and chances to travel around the country and work as a labourer shows how much Chris lived out the above quote from Thoreau.