Re: about GND problem...
As this is an RF circuit, and as you said it's operate on 45Mhz.I believe you're getting digital data bits into it or analog data,whatever. With an update rate of thousands of times per second, so in other word you have entered into radio range and things aren't gonna remain as they appear, two straight parallel wires may start acting like an antenna.Almost like in a deep African jungle, in morning it appears very pleasant, you see birds,etc, in night, it becomes dangerous, you can hear horrible noises of animals and jungle becomes many times dangerous. So you need to pay attention on bypass,decoupling,etc; When you work at RF. As all are digital bits or even if you feed 45Mhz signal with analog value, then I would say all are voltages referred to some common ground.
At high frequency this ground pin starts offering resistance, but voltage sources must have Zero impedance in ideal case, so as to reduce the impedance offered that capacitor is used in here. This is what it appears to me. You must look at mathematical model of transmission line and how it works.It's RF.I don't know exactl mathematic formulation, but It appears from the circuit, it was done so as to minimize the impedance.Look at equation of transmission line, some RF handbook, some relevant material. So you can actually calculate as how much impedance would be offered with it and without it.Because in order for this IC to opearate, it takes Input and Output, but they must have return path also, so ground is taken as return path. if Input/Output is working on RF, then ground(return path) must also be taking signal in RF.