Why do apples taste sweeter at the bottom?
For whether or not your assumption is correct, I have found the following (here), which states that sweetness indeed differs, as well as pH level:


  The bottom sections of ‘McIntosh’ apples were sweeter; whereas the bottom sections of ‘Jonagold’ were less crisp and more fruity.
  The bottom sections of both the ‘McIntosh’ and ‘Jonagold’ apples had significantly lower pH than the top. 


Fruits consist of two main parts, the pericarp and the seeds. The pericarp can be further divided into the followings: exocarp, mesocarp and endocarp. In the case of apples, the one responsible for composing most part of the fruit flesh is the mesocarp, so I would like to disregard the other two. The mesocarp consists of ground tissue almost exclusively[1] and no vascular system, thus the only way for sugars to travel inside the flesh of fruit is diffusion, which is mostly determined by gravitation, hence the result.