Nothing you stated sounds good at all. Yes, they will have to dig up the slab to find the leak. It doesn’t really take a specialist, but someone willing to take on this type of project might be hard to find.
A camera is limited to only larger diameter sized pipes. Anything is possible in your situation of where it broke. But it sounds like this project initially will be exploratory until the pipe break is found.
Definitely, make sure you make the right choice in contractors on this one, honesty is very important in not being taken for a ride at your cost. Numerous estimates is advised for your situation.
“Your best interest is secured by making the right decisions the first time.”