Well you can believe anything you want. By now you should know I don't just throw sentences out with no reason.
Setting a probe is about it's frequency response, phase response and those two combined will yield a pulse response.
Those probes have 3 trimmers. One is standard that gets set at 1 kHz, low frequency response and base probe gain. Other two, are part of a filter that is scope side, on the other end of cable. Those two will have large influence to a first 30-40ns of the pulse response. So you need, say 5MHz or smaller frequency to have a piece of flat signal plateau after that first part of the edge to be able to set it right. In which case you go with factory recommended 1 MHz, instead of pulling some numbers out of the hat.
Also you don't set pulse response to a 25 Ohm source that has 33ps risetime. Probe is not designed for that. Higher part of the spectrum will shoot trough. Don't believe?
I have at my disposition those exact probes SP3050A. I have Leo's pulser. I have two 1 GHz scopes, one of which happens to be SPS6000. And also have SDG6000X (that can do 500MHz and 1 ns pulse risetimes).
And I do have 1GHz/ 500ps pulse risetime capable source.
So it is not an opinion nor theory on my side.
As usual Mike is right. Standard is to use 3x faster edge than probe response.
As for sensitivity to edge speed, you forgot that probes are complex impedances, HF probes even more so. They will have resonances etc. How we deal with them? We try to push them higher, over frequency probe is meant to work on. There will be peaking too. So you have first trimmer that shunts divider, than cable than a box with compensator. All of that is interacting with scope input, it's capacitance and transmission line properties.. all those things together can ring like a church on Sunday..
And then you tune them up best you can. Some will prefer signal to overshoot to get that clean edge because they need to measure risetimes. Some will tune it down, making probes have risetime of 1,5-1,8ns making them 200Mhz probes but with really nice pulse response without overshoots.
But none of them will be perfect. I always chuckle when I see Nico's signature.. That is so right..