I'm aware of the fact that it is the amount of ambient light getting to the sensor determining the brightness of the background. However, there are several ways to achieve this (e.g. lower F value). It is also possible to increase the sensitivity setting (=higher ISO) to get a similar effect.
The difference between changing the shutter time and F or ISO is that the latter two affect both the ambient and strobe light to the same extend. In contrast, shutter time only affects the ambient part of the lighting because 100% of the strobe pulse will be captured even at the fastest shutter.