I don't believe it's random.
I'm level 40, have been for awhile. Been playing since day one. I've caught a ridiculous amount of mons. Everybody preaches about RNG but I don't buy it, I have too much experience. I already have 100% IV in 3 different species of Gen 4, but my best ever Venonat is 91%. That's just one example. There is no way it's "random". Convince me otherwise, and unless you wrote the code or control the servers, I'm not buying what you're selling. Some Pokemon are just nerfed, and it may be different mons for different players.
Answers
It shows when you look at a large enough sample size. Your sample size as one player is simply too small. I have 3 100% Pidgeys and 0 100% Weedles, even though the difference in their catch numbers isn't that large (7,6k vs. 5k). Is that RNG? Absolutely it is, there's no way I can claim with that small of a sample size that there's anything anomalous going on.
Dice only have six possible results, so the sample size needed to see the proper statistical pattern is somewhere along the lines of a few hundred to a few thousand (EDIT: If we're going for a statistically solid result). IV have 4096 possible results, which proportionally increases the number of needed trials.
I used Venonat for an example because they are very common and i know I've caught thousands of them. I also know that the more times I roll a dice for a specific number, the closer my chances will be to 1:6. I throw away any oddish less than 98% because I have 12 evolutions 98+ but i've never even reached 98% with a Venonat.
That defies statistical math.
If I went out right now I could catch 20 of each. I guarantee you one of the Oddish would be 80+. The Venonats would almost definitely all be crap.
After all my time playing, I know this to be a fact, I don't even have to do it.
The chance that you get at least one Oddish out of 20 that's 80%+ is 90,5%. I don't need your guarantee, if I were to catch a random 20 of any pokemon, I would expect to find one above 80% most of the time.
The Venonat is a more unlikely result. Assuming by trash you mean below 50%, we get a tiny 0,0000095% probability that each and every one of them fails to go above 50%. If you repeat that test multiple times and it adheres to your assumption, post proof and you will probably get some attention. If you then repeat it a few tens of times, you will have a solid case by which to argue that there is indeed something wrong with the RNG you're getting on Venonat IVs.
(Assuming non-WB odds for both.)
I'm in no way an expert, but I would think that arranging the game so that certain players are predisposed, if you will, to have differing odds of encountering higher/lower IVs for specific Mons than others would be a coding nightmare. With the large number of Mons out there, you're bound to have really good luck encountering high IVS of some, but not others.
I think we've all had similar experiences. For instance, I've caught 448 Houndour, 3 of them hundos. I've caught 7204 Rattata, 0 of them hundos.
If you were to roll a twenty-sided die five times, its highly unlikely yet entirely possible that you could roll a 20 every single time. On the other end of the spectrum, you could roll it hundreds of times and never roll a 20. Both instances are, of course, unlikely outliers, but they're still within the realm of possibility.
RNG can appear biased or unbelievably ridiculous, but it's still just RNG.
You don't have to buy it, but the kind of alternative you're suggesting isn't a realistic possibility either. Plus, as another user pointed out in their post, your sample size (though it may seem sizeable as an individual player) is nowhere near large enough to indicate a statistical anomaly affecting the playerbase at large.
I don't think you have. Because you're showing a clear lack of understanding of the basics. Sample size is everything, and your sample size is inconsequential. The top ranked player in the world in catches is BrandonTan91 with 450k catches and he doesn't have a large enough sample size to prove anything by himself.
As Housunkannatin already pointed out, you're the one claiming that there is an anomaly, so the burden of proof is on you to prove that such an anomaly exists. You're suggesting that the system of RNG in the game functions differently than what is recognized and accepted by the vast majority of the playerbase, including websites such as GP and the Silph Road. On top of that, you're lacking the data to support your claim. It's not up to the rest of the community to disprove your speculation.