The answer is yes. Data mining yields that RNG is based on player actions and events. To test this, I had to use an external save device, similar to what emulators use, so I could save my game mid battle. It seems all RNG in NPC battles are are determined by player in put. So I put it to a more comparable test.
Ten people battled each other on their 3DS 30 times over a few hours. They were given the same teams, all Blissey, same stats, no item, using Thunder. I chose Thunder because of its imperfect accuracy, chance to paralyze and of course, chance to critical.
Some players, however, were told to move their attack icon numerous times before attacking. Others were asked to go into their menus and move a bit, etc... Then, players were asked to attack at the same time, or as close to it as possible.
Then players were asked to do the same on battle SIM.
What I noticed in game was that the players who went into their Pokemon menu got critical hits and more hits then those that didn't, but those that circled their move list before selecting Thunder got paralysis often. It was very interesting. I also noted that when thunder was in the Top right corner, the Blissey had paralysis more often then bottom left, bottom right or top left.
On battle SIM, the results were different with completely different correlations.
I couldn't collect enough data to figure out every little thing that RNG checked, but enough at least to confirm that, in game at least, RNG is player affected. Maybe I'll go back to this study if I get the time and the funding.