Searching for the phrase "trees support each other" I found no lyrics, but some other interesting stuff, e.g. this quote from a forestry site:

Interior spruce, when growing on wet sites, does not always work very well with partial cutting. Because the roots are shallower in wet areas, and the trees support each other, spruce can suffer wind-throw when thinned too much. We are also trying small patch cuts in these stands to mitigate the tendency towards blowdown...."

Or this quote from a Woodinville, WA newspaper:

[The city planner] also explained that the City wants notification whenever someone is planning to cut a tree down. She cites a recent example of a group of trees which were cut down, leaving no wind barrier for the trees behind them. She explains that trees support each other and when the wind blows, there's a domino effect if there isn't a barrier to hold them. In the recent incident, the wind plunged several trees to the ground, having had its barrier suddenly removed.

There were also several sermons and essays that used the tree analogy to illustrate why people ought to help one another, such as this quote from the Atlanta Business Chronicle:

Hope nurtures an atmosphere of trust, loyalty and creativity. The very name connotes a sense of community, for the company is named after a tree that is the largest organism in the world. An aspen may look like a single tree, but underneath the surface, the roots form a complex network, so the trees support each other. Hope extends the metaphor to Aspen Productions: "Each individual employee is supported by the entire company."

It's not too surprising that someone would develop this idea into a song.