Does TDS qualify as a random gem spawner? Same is true for Kraken. These two have frequent anomalies reported by various players. This might be due to their popularity though, so IDK. Anyhow, if there is some link between random spawners and their resurrection/devour ability triggers, this might explain the strange results. Specifically, if these two are linked, that would make the events not independent.
Also, you cannot alter the actual pRNG result, it is only possible to alter the outcome. How is this accomplished specifically? Is the new correct outcome forced or a new pRNG output is generated and checked again in a loop to be correct?
From the point of common sense, all these considerations are perfectly valid. However, statistics and Law of large numbers do not work the same way. The array of individual pRNGs cannot be combined to form some larger pool. Local pRNG results presumably originate from a local seed and local seeds might be different for each individual process. Hence, strictly speaking, combining the pools is not possible without making some specific assumptions. However, if, for example, a random seed number is generated by a single specific server through a continuous process, this might work to an extent. Although normally, pRNG seed numbers are generated locally.
Also, as Lyya kindly explained previously, parts of pRNG are run on the server while parts are local and these certainly cannot be combined. It is not even known if the actual pRNG generators are the same.
Some pRNGs may produce more platykurtic results than others ( Kurtosis - Wikipedia ) and thus, incidence of rare and extremely rare events are considerably higher than one would normally expect. Although Mersenne Twister is not known to be particularly platykurtic, it is supposed to actually be quite uniform and passes majority of easier quality tests.
Another probably invalid comparison is GoW versus lottery. Lottery has a single true random event that determines the outcome while GoW has multiple copies of pRNG events. Thus, any low probability event still remains a low probability event no matter what. Roughly speaking, when I get that one in a million event on my personal copy of GoW, it has no relationship with what other players get on their personal copies nor it might increase the chance of this happening.
That might be coupled to ultrare event filtering as well to exclude some real anomalies. Like TDS resurrecting 8 times in a row (1E-5). However, probably, the issue of borderline might need to be balanced. A random game without surprises (pleasant or unpleasant) might be considered boring. I want these four aces on my hand. 
With regard to what specific events are considered “luck”, the list that we have had on the forum from console developers and Sirrian previously Remove Increased Luck Factor for the AI - #25 by Ozball are not specifically very rare. So, actually this type of filtering might change the outcome more frequently and more substantially than any rare event.