I'm killing time here, not advocating anything in particular...
for a pool of 20x30, you'll get 360 gallons of water in the pool for every inch of rain.
http://ucanr.edu/sites/scmg/files/30178.pdf
a pool of 20x30x5 is 3000 cubic feet, or about 22000 gallons.
Cubic Feet (ft3) To Gallons - How many gallons in a cubic foot?
to follow your bucket example, if your 22000 gallon pool gets 22000 gallons of rain water, your FC would be halved. and your house destroyed.
If your 22000 gallon pool gets 360 gallons of water (an inch of rain), that will change a FC reading of 5 ppm to 4.91. SO yes it will change the chemistry, but I think what they're getting at is the rain shouldn't be enough to drop you so far that now algae is growing. Unless you were at the bottom of an appropriate level to begin with.