Look at it this way: When a capacitor is completely discharged and you apply a voltage to it, the very first blink of an eye the capacitor voltage is zero and the current going to it is ridiculously high, so in that case the current comes first, sort of speaking.
I'm not convinced. Sounds like a measuring error to me, because a voltage of zero is no voltage and the reason it would be no voltage is because you have connected a direct short by way of a discharged capacitor across the potential. Disconnect the capacitor and I can assure you there is a voltage there if in fact you can charge the capacitor.
Voltage ~ Pressure
Current ~ Flow Rate
Starting from steady state, no pressure, no flow. Any questions? :P
Ok, you win

What do we use now to measure capactive load?
Here's what I would do:
I'd start out by measuring the resistance over whatever it's I'm out to get the capacitance on, that would be the R bit of it all, provided it's a circuit where the R and the C are attached to eachother in parallel.
Then I would subject the circuit to a low voltage AC, from a standard 60 Hz transformer, and then measure the RMS current going through it.
The current would be the RMS value of the applied voltage divided by the impedance, Z, of the circuit and Z would in turn be made out of the sum of the R and XC according to the formula Z squared = R squared + XC squared, where XC = 1/(2*pi*f*C).
So if you divide the applied voltage with the measured current you first get the impedance, then you subtract the resistance from the impedance using XC = the square root of (Z squared - R squared).
The frequency, f, is 60 Hz, so a little reverse engineering would leave you with
C (the capacitance) = 1/(XC*2*pi*f) = 1/(XC (from the above)*2*3.1415*60)
That's the short, awkward, version of it, here's the more sophisticated version,
http://www.electronics-tutorials.ws/accircuits/AC-capacitance.html