Interesting discussion. A FPS is a lot different because reactions, quick decisions and muscle memory are all going on at once so subconscious factors like colour influencing decisions seems very credible to me. On the tabletop it doesn't seem so likely since the opponent moving his red land raider forward doesn't force you to instantly decide how to react to it. With time to think between and during turns I can't imagine you'd make different decisions depending on the colour of the enemy army
Then again... I'm not so sure about that. Maybe playing against Blood Angels would make you slightly more likely to choose defensive decisions when such decisions occur. I'm struggling to think of good situations where defensive and offensive decisions are both valid- maybe the option to flat out a vehicle onto an objective or stay still and fire all weapons at full BS?
Realistically it doesn't seem like there will be an answer to this since armies are all different and unless someone had two of the same list but one painted red and the other painted blue and they then went and played a lot of games against the same opponent/s and recorded the results- how would we know?