I have been experimenting with WB for a while now, shooting raw. When you shoot, for example, in tungsten light and you take a reference image with a neutral target, the inclination is to click-WB on that target and then propagate that WB setting to all of the other images in the set that were shot in the same lighting. The idea is that this technique will neutralize the lighting color temp and neutrals will be neutral.
The essential question to consider is, why? When you actually look around a scene that is lit by tungsten light, in this example, neutral objects do not appear literally neutral. We know they ARE neutral and our brains understand this, but the object's appearance, visually, is not one of perfect neutrality. The neutral object takes on the color of the light incident upon it, including the direct light, the ambient diffuse light and any color bleed and reflection falling on it as well.
My current practice follows this logic.... Because we have evolved over many many years of seeing the world in natural daylight (as opposed to the relatively modern concept of artificial lighting) our visual systems are tuned to daylight. Therefore, the best starting point for a "natural" WB to a digital image that has no point of reference, is daylight WB. Chose one - 5500°K, 0 tint, or whatever you find works. This is what I set my camera to, regardless of the scene. You can tune the result in raw conversion, but this technique will capture the actual lighting of the scene (you can always chose to reject that rendition in raw conversion for whatever reason) in the most "natural" way that we are accustomed to seeing light and color - that is, with daylight as the "reference" lighting.
As soon as you start click-WB'ing on "something" in your scene, you bias the interpretation of the scene to the object's surface color and whatever light is falling on that object, as well as whatever artifacts in the image are present in the pixels that comprise that object (chroma noise, etc.). We have been led to believe that neutral targets and color checkers are magical tools that will make the image "correct" when, in my opinion, they tend to sterilize the image.
Try an experiment - put your camera in Daylight WB and shoot in a variety of lighting conditions with a gray reference placed in each scene. Compare the daylight (as shot) rendering to the click-WB rendering in each scene and judge for yourself which is a better rendition of the scene. I often find that the "best" result is a WB that is about half way between daylight and the click-WB color temp.
Of course there is a time and place for getting WB "correct" in terms of literal color interpretation, but I would guess those times are far from as frequent as white balance target suppliers would have you believe. Even in wedding shots, for example, where a bride's white dress is the focal point of an image, the dress does not necessarily need to be literal white, especially if the scene is light by candlelight, dance floor lighting, tungsten lighting, etc. If you capture with Daylight WB you can always dial the effect back, but if you shoot with a custom WB to sterilize the neutrals in your scene, then you have no recording of the actual lighting conditions that were present when you shot - you then have to make them up by sliding sliders.
Essentially, this technique assumes that Daylight is a "universal" white balance reference, based on how our visual systems have evolved. We visually compare everything to daylight. Tungsten is "warmer" than daylight and cloudy scenes are "cooler" than daylight.
With respect to the tint of trees, remember that when shooting in a tree-filled scene, light is filtering through and reflecting off of the canopy of the trees - this colors the light falling incident on the scene. It is like having a green-yellow filter on the lighting. It is your choice as to whether you want to keep or reject that light in your image. This scan be a particularly vexing problem when, as one often finds suggested on the internet, one shoots in "open shade" and chooses the canopy of a leafy tree as the source of shade. Skin tones are particularly difficult to get right with the introduction of green into the natural yellow of skin.
kirk