Forests, and especially old forests, deal with water differently. Rather than concentrating the water, they spread it out. The lumpy-bumpy floor of a forest, lined with spongy layers of leaves and debris and punctuated with large downed logs sends the water in all kinds of directions, and every obstacle the water hits slows it down. Slower moving water has less energy, and water with less energy does less damage.
The energy of water is what allows floodwaters to carry away big rocks and logs, and sometimes even cars and houses. A natural river system is connected to a floodplain, and when stormwater enters the river it overflows its banks into a wide flat area filled with obstacles (trees, rocks, the debris dropped in previous floods). Almost immediately after leaving its banks the water will use up its energy to spread out, and when that energy is gone it can’t carry big objects anymore, so they get dropped right where they are. This is true for smaller, forested systems too, when a stream is connected to its floodplain (and not cut into a deep channel from erosion or human alteration) it tends to drop what it is carrying quickly, just outside its banks, even in a pretty significant flood.