tps22860: Bypass capacitor layout guidelines: why a capacitor on Vout?

Part Number: tps22860

I am using TPS22860 to switch power to power-in pin Vcc of Nordic NRF51822 radio module (RedBear Nano) which draws a max of say 15mA when radio is active and more usually only 5ma when cpu is active.  The module has its own bypass capacitors on its power-in pins, totaling say a few uF.  The layout guide for the TPS22860 says use 1uF on Vin and 0.1uF on Vout.   What is the purpose of the bypass capacitor on Vout, if the load (the radio module) has its own bypass capacitors on the same network less than a few centimeters away?

I am not an EE, I have minimal understanding of switching noise, and don't have an oscilloscope.  I have been testing with a larger bypass capacitor of 4.7uF on that net, laid out near to TPS22860 pin Vout.  On Vin I also have a 4.7uF ceramic bypass capacitor laid nearby, and much larger 4mF tantalum capacitors laid only a few centimeters away (power supply storage fed by energy harvesting.)  I am assuming that larger capacitance 4.7uF  is better, but maybe I am missing something about noise?

I can't really say that my HW load switch design is causing the symptoms that I am experiencing (erratic behaviour of the SW) but I am exploring all possibilities.