First, if you examine a signal with a scope and that signal has significant energy at frequencies above the bandwidth of the scope, the result will be distorted regardless of Nyquist issues--this happens even on analog scopes. The rated bandwidth of a scope means just that, not the maximum periodic frequency of a signal that it can faithfully reproduce without distortion. The most obvious example is square waves, but the same principle applies to any waveform. The actual manifestation of the distortion is complex and varies for each particular situation.
Second, if you are referring to strong over-bandwidth signals to be displayed, aliased or not, this is nothing new or unusual. The Rigol 1054Z (hacked) will display 300MHz + signals fairly cleanly, just attenuated. If you go over Nyquist, the signal gets reflected down, but in order to be fooled by having an over-Nyquist signal reflected down to 350MHz on the SDS2000X+ with all 4 channels active, you would need a strong 650MHz signal. That's just not very likely in real-world scope use. Now if you see a 450MHz signal, you have to wonder whether it is 450 or 550, but again, a bit of real-world experimentation will show you that this is not the first thing one ought to worry about.
Third, you say you wanted a "4-channel 350MHz" scope. Frankly I have to wonder why. I really would struggle to think of a reason to use all 4 channels at once at that bandwidth, and those that I might dream up would really need some careful setup and deskewing to work. But, even allowing for the possibility that you might have such a need, I would expect anyone comparing the two scopes to notice and point out that that the Rigol lacks 50 ohm inputs. Between that and the switchable 1X/10X probes, I think you will have far more problems getting undistorted readings on the Rigol at 350MHz regardless of the sample rate being double.
I intentionally used 350Mhz and 500Mhz because we all agree that the scope goes into serious aliasing if more than 2 channels are on and a 500Mhz signal is measured by any channel. So in my example the 500MHz is not outside of the bandwidth of the scope. Therefore your point would not be applicable here as the signal is not outside the bandwidth. If we are talking about other scopes which have high energy frequencies past their bandwidth then a number of things may come into play.
1. Attenuation at the frequencies above -3db tend to attenuate much faster than before the -3db thus reducing the effect.
2. They could maintain sample rates much higher than Nyquist criteria to cover this.
3. They don't follow gaussian type.
The increase sample rate is not to cover all frequencies above bandwidth only those within a range that is not attenuated enough. All frequencies above the bandwidth will have an impact on measured signal regardless of sample rate, and we both agree on that, however the signal displayed on the scope that is under-sampled will be different than what is on the scope with proper sampling. Both will not display the correct waveform because the higher frequency will be far more attenuated, but if this higher frequency is not noise but a component of the wave then the scope showing the alias will be so off that you would have no clue as to what's happening.
Your point about the 650Mhz is similar to an experience I recently had, this is real world not theory. I was testing a RF amplifier and had a low strength 10MHZ signal feeding the amplifier, I was using my older 100Mhz scope and sine wave looked fairly normal. I switched over to the MSO5000 and noticed a totally distorted wave, I was confused and turned off the AWG and a clean 420MHz wave appeared on the display, I had seen the frequency before and immediately realized that this was coming from circuit board nearby that had been left powered on. The cable connected to the amplifier input ran close to it and amplified the signal strong enough to cause interference. My experience disproves the unlikelihood of high strength higher frequency entering your measurement, in my case the higher frequency was 42 times the signal of interest, not less than 2 times in your example. If that 420MHZ was aliased because of low sample rate then I would be searching all over to find where it was coming from because the frequency would be incorrect. Both scopes in question would not have issues with the 420Mhz but over 500MHZ the Siglent would be aliased and the Rigol would not.
I use higher frequencies to view square waves, 3 most cases. 50 ohm termination is for connection to other 50ohm devices, if I do video I would need 75 ohm. On the rare occasions I use a 50ohm termination pass through and it works fine, but a lot of circuits are not 50 ohms and a low impedance sometimes load circuit. The advantage of using the external termination is that I don't have to worry about burning out the oscilloscope's internal components since 50 ohm port is limited to 5Vrms, I can easily buy another external terminator. But again I don't need it as I don't do much RF stuff and the few are at low IF frequencies.
In summary the example I gave still stands, more than 2 channels enabled on the Siglent will be aliased by any component above 500Mhz since these are still within its -3db point and not significantly attenuated. You could if possible put in bandwidth limit filters to removed signals above 500Mhz. As it relates to the general argument about the Nyquist and frequencies outside of bandwidth which is not the case in this situation, I would have to side with the experts who recommend the sample rate to be up to 5 times the bandwidth.
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