Since they asked the prime minister for permission to pump sea water, I'm guessing that it was an option all along i.e. they have the facilities to do just a thing. The whole defence in depth concept relies on having a bazilion emergency options.

They could probably hack up a particle filter together pretty quick, but unlikely do any desalination. Any reactor which got salt water in it is very much totaled.

They don't have to use them till it's over.

The water is being boiled away, not circulated with pumps.