I don't rinse brown rice in cool water after cooking it. I cook it 1C rice in 2C water.It sounds like you like your rice with a 0.9:1 ratio of water:rice instead of 1:1. If your rice comes out too sticky then you used to much water or a bad brand. I eat rice and water in a bowl together but rinsing rice after cooking is like somebody crashing my car.
Rinsing it seemed to work good with white Jasmine rice but I haven't tried it with brown Jasmine rice.