Not exactly. Nothing is fixed in stone. There are an infinite number of solutions that fit the desired curve.
Personally, I start by selecting one of the capacitor values. It could be random, but I aim for something standard in value. Then I calculate the resistor values around that. You don't have to chose the same capacitor I do! There are hundreds of phonostage designs out there that use different values than I do. I also split the passive EQ into two separate sections. That is not necessary! You can do it in one.
Regarding the inverse RIAA circuit, as I showed above there is more than one solution. Depends on the attenuation you are aiming for. The original circuit from Lipshitz was at -44dB. I shifted it up to -40dB and added the 3.18us zero. A number of companies have copied my exact circuit and sold as their own, including York. Why don't they sell the Lipshitz instead?
FWIW - the best reason for passive EQ is how it handles overloads such as pops and tics. I believe the testing here uses steady-state sinewaves, but you really need to use an impulse instead. It makes a huge difference, especially with tube circuits. A tic through a passive EQ will just clip and then recover without delay. If the EQ is in feedback loop, what happens is that during the transient the circuit goes open loop, which causes a very audible slew distortion, plus a recovery time to get the loop closed again. That results in greatly exaggerating the tic. Better to clip and move on than to go bezerk and recover.