I should consider at least building something for 100X if I plan to play the low poer game (which IoT should really always be).
I am OK to buy, within reason…
I’m glad the BNC terminator worked as a sanity check! IMHO cheaper probes don’t necessarily mean “bad”, I have a favourite pair of cheap probes at work. The exact same brand/model/supplier has also given me probes which look and cost exactly the same in all respects, but fail the “noise with short-circuit” test as you’ve clearly shown here. But then perhaps the supplier just gave me some examples from their returns bin that day…
So I would say that cheap probes can work but you have to expect some variability from one probe to the next. It really does seem difficult to buy “professional” quality probes at a reasonable price. I once bought a set of three old used HP probes off eBay with the thought of re-making them into one or two decent ones, but I never did get around to finishing that project…
Not sure what the probe should say, but I measured the resistance of one (BNC to tip) at around 250ohm.
Keep in mind that the other critical probe performance criteria is flat, linear freq response across entire freq range. Testing this is far more difficult, but its critical unless you’re just looking at digital signals.
The probe I have here is reading only 1.1 ohms BNC shield to GND aligator clip, 100ohms from probe tip to BNC pin (switched to 1x) . It would be enlightening if you took a measurement of the good non-Rigol probe you tested earlier and compared with the Rigol probe.
Flat linear response is important to everyone, digital is still analog right? Don’t want those nice square pulses turning into sine waves 
Honestly though any probe with an aligator clip hanging off it is going to attenuate or otherwise distort any hi-impedance signal (or worse: the circuit under test itself) at “high” frequencies. Here’s a snap on the spectrum analyzer of my favourite cheap probe rated as “20MHz”:
That’s -5.76dB at the rated frequency! Cheap probes are cheap 
For comparison, here’s a 75ohm BNC cable (in a 50ohm tracking generator, couldn’t find a 50ohm BNC cable to spare):
It’s why experimenters shouldn’t be afraid to build their own custom BNC cables directly terminated onto their projects - it might be cheaper than spending $150 on a decent probe when you could achieve essentially the same low-resistance, low-capacitance path (probably better!) with $5 worth of decent RG58 cable and BNC connector at one end, and a dab of solder (or whatever) at the other.
Edit: that advice ignores the skill required and potential pitfalls of properly terminating RF connectors like BNC, it’s one of those things I’ve found takes me 2 or 3 goes each time because I only have to do it once or twice a year (and/or haven’t watched the right YouTube tutorial 
Old probes from my Trio (probe stamped Greepar)
tip->BNC ctr: 600ohm
shields: about 1ohm
Rigol
tip->BNC ctr: 300-350ohm
shields: about 1ohm
Ouch! Then I guess it has to be down to the shielding in the cable itself, or somehow the design of the attenuation switch/housing/probe assembly.