My Two Cents worth. I live in Dallas, Texas, I just spent $26K on a slab that broke and fell and it busted all my pipes in the slab and under it. I had a pipe re fit done. What a mess.
I am a staunch believer in the soaker hose therapy and with our already 9 days over 100 and no rain, I water my foundation more than my grass.
If the house was mine, I would not believe the smoke and mirrors that the people are blowing at you. If they are so confident about "no problem" then get a legal document drawn up by a lawyer and have them sign the document. See which way they run.
Stop the procedings, stop the funding, have it ripped up, or find a new home. Take pictures, document the speeches, document everything, you will sooner or later need it.
If a slab cracks now with out any weight on it and with the rains and no rain periods, just think what that crack will do. Even the locks will not stop that.
Have Ram Jack come out and jack up the slab at the contractors expense.
Man, I am furious that you were told "no Problem", what a line of $%#.