Why is it usually the case that the negative rail for ICs needs more decoupling capacitance (has worse PSRR) than the positive rail?
This is true because the LM7815 is stable with any output capacitance- the capacitor is just there to reduce the output impedance at high frequencies. Vout comes from the emitter of the NPN pass transistor. 



The LM7915, on the other hand, is made with a similar semiconductor process but has to produce a negative output voltage. Vout comes from the collector of the NPN pass transistor. It's not stable without a largeish capacitor on the output. With only 100nF on the negative regulator it will likely oscillate under some conditions, whereas the positive regulator will be fine. 

 

LM78xx


LM79xx




As far as the AD8099 goes, it probably has to do with the (internal) compensation capacitor being connected to the negative supply. Op-amps do not have ground pins generally. 

So, any change of the negative supply pin relative to 'ground' is coupled to the amplifier. 



What appears to be a pattern is actually from two quite different root causes.