"...The topic was the precipitation cycle, it wasn't about the total amount of water here on earth in any form...."
increased heat = Increased evaporation Increased rain volume increase in ice melting, leading to increase in sea levels. More "matter" being added to the cycle from ice that wasn't previously melting.
You were wrong in your assumption about the precipitation cycle not getting an increase in "matter" from additional meltingce. The seas are getting additional water from the increase in ice melting, so it isn't a consistent amount of "matter" in the cycle.
Nothing to assume here, increase in rain volume leading to flooding.
