The reason that SHx floats is due to the high-side gate architecture. When the low-side FET is not on, the leakage from SHx will have no path to ground which means that SHx will float up to VM, through the body diode of the FET, as shown in the diagram below. In the case where a resistor divider is present on SHx, not all of the voltage will float up to VM as some of the current will flow through the added resistor divider.
When both the low- and high-side FETs are not on, GHx is essentially shorted to SHx. This means that GHx will also float with respect to SHx. However, just because a voltage is seen on GHx, does not necessarily mean that the high-side FET is being turned on. What determines whether the high-side FET is on, is the voltage of GHx with respect to SHx (VGS). For example, if GHx is 12V and SHx is 12V, the differential voltage between GHx-SHx is 0V, which means that the FET is not on and the output for GHx is off. In order to turn on the high-side FET a voltage differential of at least 10-12V (GHx-SHx) is needed.
