It is very unusual for a software system to be truly independent, without any need to interact with other systems or components. So whilst it is important to ensure that your solution runs correctly in its own right, some consideration needs to be given to how successfully it interacts with other systems.
For example, when making a ballpoint pen, each individual part, such as the cap, body and button mechanism, will all be produced and tested separately. When each of these parts have been produced they will be assembled and tested to see if they work together in the correct manner. After all, just because the process to make the cap has been followed to the letter and it has passed all of its individual test, it does not guarantee that it will fit onto the body.