Yes, it does hurt to plant fruit trees close together. 

More Info: The main downside to planting trees too close together is that it leaves less than adequate room for each tree's root structure. If there is a lack of unobstructed subterranean area, tree roots can get truncated, tangled, and blunted.

The Supremacy of Sequoias

A good reminder of just how critical it is for tree roots to have room to grow is the natural evolution curve of California's majestic sequoia trees. Even though these trees can last hundreds of years, it is within the first few years of their growth that the root structure is most rapidly expanding.

Some sequoia tree roots can spread out to a distance of up to 200 feet when fully grown, a truly remarkable distance. All told, a single sequoia tree can impact up to four square acres of land arount its base, to support its rank as the United States' (and world's) most impressively rooted tree.

However, as anyone who has visited a sequoia national forest can attest, these trees naturally were able to grow without being apart the full distance of their maximum underground root reach. So nature's answer to the question above is one of a happy balance; not too close, but also not necessarily too far from one another.

A Thousand Points of Might

Another way to grasp the intricacy of tree roots is to consider that in some cases, a tree's underground grasp can run hundreds of kilometers in total, and thousands of root tips. There are all kinds of scientific measurement techniques that involve the quantification of tree roots. One, known as the "root area index," is calculated by tabulating the number of grams of roots present in vertical samples of soil.

The analysis of the tree roots for a healthy 60-year-old maple shows that it was able to thrive even though it coursed under nearly a dozen other similar trees. The science of spacing tree plantings is dependent on the type of tree, most of all.