Perhaps a different situation, but maybe I might refer to this pretty recent post of an obviously knowledgeable person. The screenshot probably shows "raw data samples connected by lines" and not what I would recognize as a "true signal reconstructed from data points within bandwidth". Although it is a single shot and no average. At 20ns/div I would expect overshoots on the edges and a much smoother top, even with 250MHz bandwidth and 1GS/s. The measurements certainly do have signal noise and at least 1Bit digitizing noise but that shouldn't necessarily get translated into a jaggy line showing edges and corners way beyond the bandwidth. There is no thing like "corners" in signals.
Clicking the link doesn't work for me and if I copy the stripped link into the browser, I'm landing at reply #2353 which doen't contain any screenshot.
So I assume you are referring to reply #2356. I do not know about the settings – but that is what you get on an (only) 8-bit scope, where each sample is represented by a line that is 2 screen-pixels high. The signal is slow (10 MHz), obviously noisy and I honestly don't know how BillyO managed to show a single frame even though the DSO says "Trig'd" (1). Normally, we see hundreds or even thousands of acquisitions (records) mixed together in a single frame, 60 times per second – except when in Stop mode, where only the most recent record is shown. The rest is in the history.
How do you know it is linear interpolation? I don't think so – even though it would be the most appropriate display mode for digital (square) signals. When looking close, we just see the granular noise of +/-1 sample, which is represented by +/-2 pixels on the screen. Absolutely no way to determine which interpolation method was used. Furthermore, there are 280 points (samples) in this screen, hence not much need for interpolation.
And why would you expect overshoots at the edges? How can you know what the original signal looks like? Only crappy oscilloscope frontends produce a lot of overshooting on a clean square wave. And I assume that BillyO used a clean signal for testing his "improved" scope…
And "a jaggy line showing edges and corners way beyond the bandwidth": the granular noise of an ADC stems from the sample rate, not the frontend, hence the input bandwidth is irrelevant. One horizontal division represents 20 ns. I cannot see more than 20 different levels within one division, so this would be perfectly plausible for 1 GSa/s and a granular noise of +/-1 LSB.
Here are a few examples how fast signals at short time bases look like with a proper setup, so we can benefit from the SPO technology:
First a 400 MHz sine, vastly exceeding the bandwidth of the 300 MHz DSO (Siglent SDS2304X back in 2016), demonstrating its measurement capabilities (and accuracy). This is about time resolution, but also nicely demonstrates signal reconstruction. Only 1 ns/div and 28 points record length, reply #68:
https://www.eevblog.com/forum/testgear/will-keysight-upgrade-the-2000-3000t-x-series-oscilloscopes-within-a-few-months/msg1029057/#msg1029057Then a modulated signal in Dots mode (SDS1104X-E, 2017), to demonstrate that interpolation or reconstruction aren't even necessary in most cases, guaranteeing the best signal fidelity of all methods. This was about a different behavior on signal drop out in normal trigger mode, which I found fine back then, but Siglent have altered it in later firmware to be more mainstream. 50 ns/div, dots mode; reply #341:
https://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/msg1359013/#msg1359013Finally a number of square waves at 10 ns/div (SDS1202X-E, SDS2304X, 2018), clearly demonstrating how noticable the difference between a 200 and 300 MHz scope can be in certain situations (the actual bandwidth of the SDS2304X is up to 450 MHz, depending on the probes), reply #515:
https://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/msg1433299/#msg1433299While these data points might have been measured just so, they most likely have to get correlated first to get a better representation of the underlying true signal they had sampled - which than may take advantage of a higher vertical resolution than the 256 different discrete values an 8Bit digitizer might collect. Maybe the scopes CAN do that, but nobody uses such a function for certain reasons. I know that it can be done on modern scopes for multiple waveforms in a greyscale or color manner to smooth out statistical variations.
In contemporary Siglent machines we get the original raw data when using normal acquisition and dots display mode. Only when the timebase gets so slow that the scope cannot maintain the full sample rate anymore, then the input sample rate gets decimated after the fact, but the remaining samples are still unmodified.
Decimation algorithm is different when using Peak Detect, which also destroys the signal integrity hence is a mode only for tinkerers or service techs, but not for people who want to do serious signal analysis. Thankfully, the deep memory of modern DSOs vastly reduces the situations, where peak detect would be useful.
There are more acquisition modes, like Average and ERES, both modifying the original samples. The SDS2000X Plus implements these modes as math functions, so we can use them while still preserving the original data. Better scopes (starting from SDS2000X HD) offer both (Average and ERES as acquisition modes and math functions) at the same time.
Like the acquisition modes, we can select the display modes: raw dots, linear interpolation or sin(x)/x reconstruction.
Without decimation,
all samples make it to the screen, used for intensity or color grading, as especially the modulation example above should have revealed already.
I have not yet found a suitable discussion that/why this might be the only viable method of displaying the samples, but I still have a few thousands of Posts to read. 
But I do believe I have not seen a "reconstructed signal" so far on any DSO topic.
Regarding a discussion about "reconstruction", may I recommend this review, where this topic (and many more) are discussed in great detail, with lots of screenshots for demonstration.
https://www.eevblog.com/forum/testgear/siglent-sds1104x-e-in-depth-reviewBeing mostly analog with my measurements so far, I might have to get used to different expectations in the DSO world.
This was certainly true in the last century, where DSOs really left much to be desired and analog engineers mistrusted them. Slow sample rates, short memories, the attempt, to overcome this with ETS, which works only for stably triggered periodic signals – but for longer periods, the scope also needs more memory – and sin(x)/x reconstruction was indeed not so common, because the lack of computation power …
Nowadays Analog engineers can get perfectly happy with the contemporary machines, all the more so if they choose 12 bit instead of just 8. Thankfully so, because the old analog boat anchors can't be ordered anymore anyway. Instead of this, analog engineers benefit from the massive increased capabilities, like automated measurements, advanced math including a properly implemented FFT and bode plot applications, which can replace a signal analyzer in quite a few cases.
(1) EDIT: Well, there is a way to disable the SPO engine ... by selecting "slow acquisition" in the Acquire menu. Maybe that's what happened here.
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