Ok - here it goes (sorry for being so verbose),
Most touch screens these days are capacitive touch screens so that they work by detecting the electrical charge provided by our fingers. In a nutshell, the stylus needs to transfer electric charges from your finger to the tip of the stylus where it interacts with the electric field of the capacitive touch screen.
Here is how a capacitive touch screen works. The basic capacitive touchscreen is essentially two layers of conductors with stripes running horizontally on one and vertically on the other. Usually the conductors are not just straight lines, but have a pattern to them to maximize their coverage. So the light passes through them, the conductors are typically made from Indium Tin Oxide which is a transparent conductive material that is coated on the surface (usually of glass) and then is photographically/chemically etched off in select areas to form the pattern - much in the same way that copper is etched away from a substrate to make printed circuit boards. There is also a thin transparent insulating material between the two layers.
One row, the driver, is connected such that it has a given electric current applied, usually scanned across rather than having all of them energized at the same time. The other row, the sensor, detects the electric current. The insulator between them forms a capacitor (by definition a capacitor is two conductors separated by an insulator). The current through the driver layer produces a negative field which induces a positive field in the sensor layer.
Since our bodies are relative good conductors, when our finger approaches the screen, it interacts and disrupts the electric field in the sensor layer by changing the amount of positive charge on the sensor layer. This change in charge changes the capacitance of that specific area. It is this change in capacitance that is detected, measured, and located on the grid. This change is interpreted as a touch input in a specific location (x-y coordinate) on the screen.
A stylus is intended to work as an extension of our finger. It needs to be a conducive object that disturbs the electric field on the touch screen just like our finger would. The little rubber tip of the stylus is made from a conductive rubber material (usually carbon impregnated). In other words, some kind of electrical contact with our body is needed to make the stylus appear as an extension of our finger. In addition to having a similar amount of conductivity as our finger, and since our fingers are not pointy, the stylus tip needs to be a little rounded (not pointy) too.
Most commercial styluses in the market either have a metal body or have metal components that are exposed on the surface that connect internally to the stylus tip. When one holds the stylus the electric charges from our body are extended to the stylus tip which then interacts with the electric field on the touch screen to generate the touch input.
So, the brass tube acts as a conductor from other parts of the pen/stylus to connect your bodies conductivity to the stylus tip.
I hope that helps answer your "why" - Dave