This could be interesting an interesting debate.
With all due respect where do you think these facts are going to come from ? Flight training providers tend not to keep records of people who don't get jobs although this wouldn't be a bad idea, it's not just US flight schools that tell you what you want to hear. UK flight schools often employ sales staff for a very good reason and it's not just to answer the phone.
I have yet to meet one single CPL IR ME that has not got a job flying and gave up looking to find another job and never retun to fly again. So yes, flight schools may be correct when saying that all their students find a job.
Where many flight schools are lying to you is when they show you all these very nice pictures of shiny jet airliners on their website telling you that that is what you're gonna get 200 flight hours later.
Otherwise there's plenty of jobs out there.
I know of a couple of bizjet operators who are not using their aircraft at capacity as the pilots they have are not sufficient.
Flight schools are begging for instructors.
The only problem with these kinds of jobs is that you don't get paid the same and it may not be what you were aiming for. On the bright side, type-ratings are alot cheaper and routine is not part of the daily equation.
If you find a nice place, you can be treated as being part of a family.
Patience will reward you.