Since I'm not the only one having this behavior, I think it's not a hardware defect.
I am more convinced it may be a firmware bug also because now I can no longer generate the distortion, even by doing the procedure listed by me.
Now the problem occurs both in Hiz and 50 exceeding the threshold of 1Vpp at 50 Ohm.
I don't know now 
I understand what the reason is!
The change in load setting only results in coincidence.
The real reason why the square wave sometimes comes out "clean" or distorted is due to the voltage range that the generator uses.
In fact, exceeding the value of 1Vpp by 1 mV even with load set at 50 Ohm, distortion occurs.
If you set the output to 995 Vpp 50 Ohm and then set Hiz there is no distortion.
Obviously, the variation of the waveform (distortion) due to the change in gain of the output stage occurs for the threshold value of 1 Vpp and via software when the output is activated there is a different setting of the output gain due to different approximations in the calculations.
Independent of load value selected (what can be what ever between 50 ohm to HiZ) we need just think final amplifier level. There is small changes when it is working in different output voltage bands. I do not remember these thresholds where system change level band. Between these ranges there is small differences in edge response. I have tested it and it is nominal to this and not failure/error. As oscilloscopes also generators result is sum of errors. There is not ideal machines instead of school books.
Now it depends of course what kind of compromises tghere have done in circuit. All can do nearly - nearly - perfect instrument if have infinite amount of bank notes for it. Even I can. Question is how cheap can done instrument what still is acceptable in performance in its price segment.
With all these anomalies it well meet its specs. What other it need meet.
After then users use these and when users use they add own errors when they measure these with not ideal scope and signal connected with not ideal matching. Also SDG output true impedance, what is ALWAYS nominal 50ohm DC impedance +/- something and after then some reactances.
Just need understand real practice and reality. All can be better .. but...
Now sum together all error marginals (scope, sdg, signal pathway between, in your known environment) and make worst case calculus and best case calculus and for all parameters and think between these is "window" where inside need stay. After then look if your result is inside this "window". if this match without breaking window borders all is ok. If still not ok, then you have wrong instruments for your needs. Period. Real world is not perfect.
But also then, if results do not stay inside this previously used "window" thebn need be alarmed and then need look what is out of order and perhaps need repair etc.
Remember, what ever External Load set in SDG settings its output impedance do not change.
So if select
Case 1. 50ohm and set voltage level out example 1Vpp it is 1Vpp IF external load is perfectly 50ohm and only then.
Case 2. if then set HiZ and also external load is HiZ and set output is 1V, it is 1V IF external load is perfectly HiZ..
But in Case 1. SDG internal end aplifier output is 2V
and in Case 2. SDG internal end amplifier output is 1V
But in both cases, using right Load, user see with oscilloscope this 1V.
Now all understand that SDG works with different internal output voiltage and this may lead to bit different square or other wave shape. Specially if these two voltages are in differen internal voltage band (you can listen these relays change)
And as just told, it is NOT perfect ideal machine. So there is differences and no need wonder. Least I do not wonder. Even when I think it can do perhaps better without high rise in retail price.
But products must also be in its performance / price segment and not competite example with same manufacturer more expensive segment products, what it partially now done, if we look some small part of functions separately. Example more expensive SDG2000X can not do this kind of square wave. It do not at all have this.
Of course SDG1000X can not what many things SDG2kX can but square/rectangle it beat it.
It was also small surprise Siglent add TrueArb feature tiny version to SDG1000X just in one previous FW update.
Also for users who use it as rf generator they time ago change level handling when AM modulation. Now if you turn AM mod on or off or change modulation depth it keep constant carrier level as all serious conventional rf generators have done tens of years.
Many things can do inside FW but some are in HW circuit and thats it. Just like this small changes in square shape over whole voltage range. it change and it need accept. If it is broken, out of normal, then need repair or factory cal depending problem.
Times ago I have very expensive (and heavy, made like tank and inside pure gold more than little) HP programmable pulse generator. And also its pulse edge change some amount when pulse level change and more when it move to some next level voltage band. Also overshoot change some amount and sure it was not due my scope. Also signal pathway from generator to scope was best possible Huber Suhner cable what short cable price is perhaps ten of SDG1000X. But this expensive generator pulse was still inside specs. Not at all ideal perfect but, inside specs. If I try use grade C specs instrument for grade B needs I am wrong not instruments. Opposite way is - expensive but easy.
Important is now just look if OP SDG is normal ok or if it have problem or if user have problem in his thinking or his other things used for testings. Nearly all is possible.