Analog Switch, switch a voltage that is ~0.5v higher than VCC
Of course it affects the signal if it is above Vcc. 

Why do you think the fact that "these ICs are just using MOSFETs internally" is a reason that Vcc shouldn't be the upper limit for the signal? 

Image borrowed from Maxim application note 5299:



The surrounding n-substrate (or n-well) of each P-MOSFETs is connected to Vcc (see the "body" connection on the diagram above). So each p-MOSFET forms a diode from the p-channel to Vcc. If the signal is higher than Vcc + 0.6V the diode gets forward biased (turns on; i.e. signal current flows to Vcc). 

Vcc + ca. 0.5V is already too high to have no current flowing through the diodes.

In addition there's probably a pair of Schottky-diodes for protection at each input and output: one going to Vcc and one coming from GND. Their forward voltage is even lower: 0.3V.