There are always algae spores in the pool, in the air, on the deck etc.. Chorination just keeps them from growing. The sock is in constant contact with the pool water, so algae won't grow if the pool is properly sanitized. If algae can grow on the sock, it can grow anywhere in the pool.

The string on my thermometer had a healthy blue-green crop on it above the water line earlier this summer, so I tied it on the ladder one step lower. Now it's white.