I tested the probe today and it seems my scepticism in the original post was unwarranted - its frequency response is not bad at all, considering it sells for about 35 USD. I used 1 kHz sinewave as base and I got this frequency response:
1k 0 dB
100k 0,08 dB
1M -0,15 dB
10M -0,51 dB
20M -0,69 dB
40M -0,82 dB
60M -0,52 dB
80M 0,14 dB
100M -0,49 dB
120M 0,31 dB
There is a small ripple around 100 MHz, but it's within 1 dB, which is negligible for most high voltage measurements. Then I pulled apart the BNC box and it was immediately clear how they managed to get such good results: they tune components for every probe by hand. There are two resistors and one trimmer cap. The first resistor is in series with coax center conductor and tunes the overall voltage ratio of the probe. This is why the probe has exact 1:100 ratio even though the large resistor in the tip has 105M instead of expected 99M. The second resistor is in series with the trimmer cap and is tuned for best response at higher frequencies. In my case, the resistors have obscure values of 113R and 42R2. My colleague noted the PCB looks like it was soldered on several times, so it's possible they tried a few different values before settling for these two. In any case, the metal base under the PCB looks surprisingly robust, so it shouldn't break too soon.