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.
But it is outside the rated bandwidth, which is 350MHz when both channels in a pair are on. I don't know if Siglent actually reduces the bandwidth in some manner in this instance--I would hope that they would. And if I'm not mistaken, there is an additional 200MHz bandwidth limiter on the higher frequency models. I would probably engage that any time I was using more than 2 channels.
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.
The first part is exactly correct. I'm not sure what you mean by displaying the correct waveform or being so far off that you have no clue. Oscilloscopes rarely display anything worth looking at in an 'exactly correct' way. In any case, unless your sample rate is 2X the highest frequency component present, you'll have issues of some sort or another.
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.
Here I think you've misunderstood--I didn't say you wouldn't have higher frequencies than you expect. Your stray signal was 42X the 'test signal but was still within Nyquist of the Rigol and just barely out of the rated bandwidth and apparently quite strong relative to the desired signal. There's no expectation that it would be suppressed nor would it be reflected down by either scope in question. B/T/W, your 100MHz scope handled it just fine, right? What was its sampling rate? If it were 250MSa/S, would you have seen aliasing? Let's say your signal was 520MHz and you were running the Siglent in 4-channel mode. Whatever part of it was not attenuated would fold back to 480MHz, which would be 'wrong'. The only question would be how well the scope attenuates this over-bandwidth signal and I don't have one to test. My experience with other Siglent and Rigol models suggest that they don't handle approaches to the Nyquist limit very nicely at all. I've mentioned this before and user rfloop pointed out, among other things, that this was a necessary consequence of maintaining a good step response and that it wouldn't be an issue in most real use cases. Yes, as I have myself demonstrated, strong over-bandwidth signals wreak some havoc on these scopes and it is best to stay as far away from Nyquist as possible. I've referred to my SDS1(2)04X-E as an excellent two-channel scope because at 1GSa/S it handles over-bandwidth signals reasonably well but at 500MSa/S, it looks terrible. It hasn't shown up in a real-world example for me yet and for your example, while I guess it is 'real world', it's not something I'd worry about too much as I don't expect a scope to solve every problem. Besides, what would happen if that signal was 1.1GHz? More samples are great--with this I agree--but there's always some weird thing that can happen.
I use higher frequencies bandwidth 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.
On my Tektronix scopes that have 50R inputs, if you overload them they switch back to 1M. You can always just use the 1M setting with a 50R (or other) external terminator, but the step response won't be as good, or at least it certainly isn't on my 2465B. If your square waves look good enough with an external terminator, then you probably don't need 350MHz bandwidth... I would hope that Siglent also disconnects the internal 50R termination in case of overload, since they have to have the relay for it anyway. If they don't do this then they should.
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.
More samples is better, no doubt. They also can make up for shortcomings elsewhere in the design. If Siglent had 2GSa/S for each channel, they might arguably have a better product--but then it would cost more as those ADCs aren't cheap. Rigol has gone their own way with their custom chipset that has a very high sampling rate at a lower cost, but with some real compromises. It would be interesting to see a head-to-head comparison of their actual analog display performance.