I perfectly agree. Its simply the gauss normal distribution, not more or less. Just enjoy the game and party when you get a HR. And if not, simply trade 
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I just see that the argument you made is that since we do not have truely independent randomness, this might explain correlated drops like your example of two Jahs in a row. Interesting thought. Actually your hypothesis would be testable with flawless gem drops coming only from one source, e.g. high council or even better duriel. (Actually all the low drops could be used.)
On the other hand, when, lets say the random calculation starts e.g. with the rpm of your cpu fan, it would take 2 times exactly the same rpm when calculating the drop. Extreamly unlikely, but possible. Like Terry Pratchett used to say " “Scientists have calculated that the chances of something so patently absurd actually existing are millions to one . But magicians have calculated that million-to-one chances crop up nine times out of ten.”
The gem experiment sounds good. I have 3/4 stash full with flawless gems comming from tz cows. When its full, i count each type. Although, the sample size could be to small.
I think its good to keep in mind, that real random numbers will come with quantum computers.
But considering your two Jahs, wouldn’t that mean that the seed starts new for each game? Nobody knows. There was an experiment years ago where a tool would set the system clock for every cpu cycle if I remember right, and suddendly you had fixed drops and fixed monsters for each new game.
For gem drops, bosses have a different drop rate, so collecting from normal enemies and bosses would skew results. Ideally the drops need to come only from sources with equal drop chances, or even better, only from one specific enemy. Nevertheless I believe cow gems are a good test.
Oh yes, i think we mean the same i guess its some kind of hybrid random generator useing some variables like fan speed, temp, clickspeed of your mouse etc. as seed. And somehow these variables were the same in a row. But since this happening occured only once as long as i play, it seems to be very rare i guess it would be a great topic for a scientific paper
My main argument against methodic deviations always was, that if there really would be something reproducible, it would be widely known, and it would also be in Blizzards interest to fix it. On the other hand you can explain everything with true randomness. It is only relatively cumbersome to prove with drops only. The coders which where present in the 2000’s have now other things to do
At the end it will be something like randint() or rand() or some command like that. And its perfectly ok. Maybe the circumstances are somehow similiar in a row of drops but why bother 
if one could manipulate the algorithm, the skinner box would instantely become dysfunctional and thus the game become boring if you know, that a certain monster drops every time the same loot. Imagine diaclone to drop a 20/20/10 every time…