Electronic – Why do we use S-parameters for High frequency signals

As you suspect, the input capacitance will be forming an RC low pass filter with the resistance.

Let's assume 2pF for the input capacitance (reasonably typical for a FET input opamp)

With your 681k resistor it will form a filter with a -3dB point of:

1 / (2pi * 681k * 2pF) = ~117kHz

So the square wave of 125kHz will not look very square at all, since it's harmonics will be attenuated.

Note this does not include any additional capacitance from your layout (traces etc)
As Olin points out the actual rolloff frequency is likely to be quite a bit lower (how much depends on your layout)

The input impedance of a non inverting FET opamp will be very large anyway (> 100 Megaohm)
Why do you need the 681k resistor? (a schematic of your setup would help)

If you do need the resistor (e.g. as part of a voltage divider) then you can add a small amount of capacitance across it to compensate for the roll off (you will need to do the calculations to work out how much)
For examples of this, I suggest googling for/looking at oscilloscope input circuits.

is it normal to get false results with those probes (or voltage dividers) on high-frequency voltages?

Yes, without a proper frequency compensation. It happens because resistors have small parasitic capacitance, which can be modelled as a capacitor in parallel with a resistor. These parasitic capacitors form a capacitive voltage divider for high-frequency signals. If the ratio of the parasitic divider differs from the ratio at DC, you will get wrong measurements, since the overall ratio becomes frequency-dependent.

Usually this is not a problem at kHz range. But not in the case of high voltage, which implies high-value resistors. The capacitance of a typical resistor is approximately 1.5 pF, which gives 3.3 MΩ at 32 kHz for a pure sine wave. Because you are using high-value resistors, the parasitic capacitance becomes the dominant factor even at kHz-range frequencies. If a signal is not a pure sine wave, i.e. it contains high-frequency harmonics, the parasitic capacitance dominates even more.

Do deal with the problem, add a compensating capacitor (typically, it is a variable capacitor). To get a frequency compensation the following condition must be met $$\frac{R_2}{R_1 + R_2} = \frac{C_1}{C_1 + C_2}$$

This can derived from the ratio for a capacitive divider $$\frac{\frac{1}{j\omega C_2}}{{\frac{1}{j\omega C_1} + \frac{1}{j\omega C_2}}}$$

The easiest way to test a divider is to look at a divided square wave signal via an oscilloscope. With the right compensation, the square wave looks like the scaled square wave. Without the right compensation, your will see a signal with a strange shape. That's because the ratio of uncompensated divider depends on a harmonic number, and after the division the harmonics do not sum up to the square wave.

I'm not sure that the frequency compensation is the only problem; probably there are other issues related to a noise in the measurement circuit.

Also, typical 1/8W resistors are not suitable for 1.2 kV RMS. The maximum allowed voltage for such resistors does not exceed 100 V RMS, if I remember correctly. Consult the datasheet for the exact value.

edit

One way to get proper division is to use 10 nF capacitor as a part of the divider

^{simulate this circuit – Schematic created using CircuitLab}

Note that $$\frac{100\,\text{kΩ}}{10000\,\text{kΩ} + 100\,\text{kΩ}} = \frac{10\,\text{nF}}{10\,\text{nF} + 1000\,\text{nF}}$$