I neither say it was a rule, nor that plants couldn't be grown with lighting of another color temperature.
6500 = pretty nice, average, appealing to the eye. People recommend lighting in the 6500k range purely because it appears fairly natural to the naked eye in a tank.
When someone is new to lighting, most people in this hobby try to steer them toward something that looks a lot like natural daylight. As the OP said, their light looks orange/yellow.
This is not true. 2300K, 3200K, 4100K, 5000K, 6500K, 7500K, 8000K, 10000K... I've grown lush plants with all of them. All you need is enough of the kind of light you are providing.
My personal preference is 4100K, smooth spectrum.
I'm not sure why this 6500K "rule" keeps being passed around. I'm guessing it's marketing.